Quantum Information and Quantum Computing

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.5	5.3	2011	17.8 Days	CHF 2400
Electronics electronics	2.6	5.3	2012	16.8 Days	CHF 2400
Entropy entropy	2.1	4.9	1999	22.4 Days	CHF 2600
Mathematics mathematics	2.3	4.0	2013	17.1 Days	CHF 2600
Symmetry symmetry	2.2	5.4	2009	16.8 Days	CHF 2400

11 pages, 812 KiB

Open AccessArticle

by Longhan Wang, Yifan Sun and Xiangdong Zhang

Entropy 2023, 25(7), 1090; https://doi.org/10.3390/e25071090 - 20 Jul 2023

Cited by 1 | Viewed by 1556

Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, [...] Read more.

Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, we introduce the notion of quantum adversarial transfer learning, where data are completely encoded by quantum states. A measurement-based judgment of the data label and a quantum subroutine to compute the gradients are discussed in detail. We also prove that our proposal has an exponential advantage over its classical counterparts in terms of computing resources such as the gate number of the circuits and the size of the storage required for the generated data. Finally, numerical experiments demonstrate that our model can be successfully trained, achieving high accuracy on certain datasets. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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14 pages, 456 KiB

Open AccessArticle

Noisy Quantum Channel Characterization Using Quantum Neural Networks

by Junyang Song, Bo Lu, Lu Liu and Chuan Wang

Electronics 2023, 12(11), 2430; https://doi.org/10.3390/electronics12112430 - 27 May 2023

Cited by 1 | Viewed by 2038

Abstract

Channel noise is considered to be the main obstacle in long-distance quantum communication and distributed quantum networks. Here, employing a quantum neural network, we present an efficient method to study the model and detect the noise of quantum channels. Based on various types [...] Read more.

Channel noise is considered to be the main obstacle in long-distance quantum communication and distributed quantum networks. Here, employing a quantum neural network, we present an efficient method to study the model and detect the noise of quantum channels. Based on various types of noisy quantum channel models, we construct the architecture of the quantum neural network and the model training process. Finally, we perform experiments to verify the training effectiveness of the scheme, and the results show that the cost function of the quantum neural network could approach above 90% of the channel model. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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15 pages, 6465 KiB

Open AccessArticle

Quantum Image Processing Algorithm Using Line Detection Mask Based on NEQR

by Tao Li, Pengpeng Zhao, Yadong Zhou and Yidai Zhang

Entropy 2023, 25(5), 738; https://doi.org/10.3390/e25050738 - 29 Apr 2023

Cited by 4 | Viewed by 2498

Abstract

Line detection is a fundamental technique in image processing. It can extract the required information, while the information that does not need attention can be ignored, thus reducing the amount of data. At the same time, line detection is also the basis of [...] Read more.

Line detection is a fundamental technique in image processing. It can extract the required information, while the information that does not need attention can be ignored, thus reducing the amount of data. At the same time, line detection is also the basis of image segmentation and plays an important role in this process. In this paper, we implement a quantum algorithm based on a line detection mask for novel enhanced quantum representation (NEQR). We build a quantum algorithm for line detection in different directions and design a quantum circuit for line detection. The detailed module designed is also provided. On a classical computer, we simulate the quantum method, and the simulation results prove the feasibility of the quantum method. By analyzing the complexity of quantum line detection, we find that the computation complexity of the proposed method is improved compared to some similar edge detection algorithms. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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24 pages, 479 KiB

Open AccessArticle

Quantum Pattern Classification in a Three-Qubit System

by Menna Elmasry, Ahmed Younes, Islam Elkabani and Ashraf Elsayed

Symmetry 2023, 15(4), 883; https://doi.org/10.3390/sym15040883 - 8 Apr 2023

Cited by 2 | Viewed by 1377

Abstract

The problem of pattern classification in quantum data has been of great importance over the past few years. This study investigates the effect of deploying Grover’s, the partial diffusion, and the fixed-phase algorithms separately to amplify the amplitudes of a desired pattern in [...] Read more.

The problem of pattern classification in quantum data has been of great importance over the past few years. This study investigates the effect of deploying Grover’s, the partial diffusion, and the fixed-phase algorithms separately to amplify the amplitudes of a desired pattern in an unstructured dataset. These quantum search operators were applied to symmetric and antisymmetric input superpositions on a three-qubit system for 20 iterations each. After each iteration, different probabilities of classification were calculated in order to determine the accuracy of classification for each of the three quantum search operators. The results indicated that, in the case of applying the three quantum search operators to incomplete superposition input states, the partial diffusion operator outperformed the other operators with a probability of correct classification that reached 100% in certain iterations. It also showed that the classification accuracy of the fixed-phase operator exceeded the accuracy of the other two operators by 40% in most cases when the input state was a uniform superposition, and some of the basis states were phase-inverted. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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16 pages, 1821 KiB

Open AccessCommunication

A Cryogenic 8-Bit 32 MS/s SAR ADC Operating down to 4.2 K

by Yajie Huang, Chao Luo and Guoping Guo

Electronics 2023, 12(6), 1420; https://doi.org/10.3390/electronics12061420 - 16 Mar 2023

Cited by 3 | Viewed by 2390

Abstract

This paper presents a cryogenic 8-bit 32 MS/s successive approximation register (SAR) analog-to-digital converter (ADC) which operates down to 4.2 K. This work uses a modified liquid helium temperature (LHT) SMIC 0.18 μm CMOS technology to support the post-layout simulation. The proposed architecture [...] Read more.

This paper presents a cryogenic 8-bit 32 MS/s successive approximation register (SAR) analog-to-digital converter (ADC) which operates down to 4.2 K. This work uses a modified liquid helium temperature (LHT) SMIC 0.18 μm CMOS technology to support the post-layout simulation. The proposed architecture adopts an offset-promoted dynamic comparator, waveform shaping circuit and true single-phase clock (TSPC) based sar logic circuit to achieve high realizing frequency and low power dissipation. At 1.8-V supply, 1.7 V input amplitude and 32 MS/s sampling frequency, the ADC achieves a power consumption of 2.4 mW and a signal-to-noise and distortion ratio (SNDR) of 47.7 dB, obtaining a figure of merit (FOM) of 378 fJ/conversion-step. The layout area of the ADC is about 0.253 mm

^{2}

. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 1161 KiB

Open AccessCommunication

Entangled Frequency-Tunable Microwave Photons in a Superconducting Circuit

by Kaixuan Zhang, Chunhai Cao, Jian Chen, Huabing Wang, Guozhu Sun and Peiheng Wu

Appl. Sci. 2023, 13(6), 3688; https://doi.org/10.3390/app13063688 - 14 Mar 2023

Viewed by 1783

Abstract

We propose a frequency-tunable source to emit entangled microwave photons on the platform of a superconducting circuit, in which two superconducting transmission-line resonators are coupled via a capacitor and one resonator is inserted with a superconducting quantum interference device (SQUID) in the center. [...] Read more.

We propose a frequency-tunable source to emit entangled microwave photons on the platform of a superconducting circuit, in which two superconducting transmission-line resonators are coupled via a capacitor and one resonator is inserted with a superconducting quantum interference device (SQUID) in the center. By pumping the circuit appropriately with an external coherent microwave signal through the SQUID, microwave photons are emitted in pairs out of the circuit. The entanglement between the two modes is demonstrated by numerically calculating the second-order coherence function and the logarithmic negativity of the output microwave signals. Due to the tunability of SQUID’s equivalent inductance, the frequencies of the entangled microwave photons can be tuned by an external flux bias in situ. Our proposal paves a new way for obtaining entangled frequency-tunable two-mode microwave photons. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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14 pages, 1176 KiB

Open AccessArticle

Variational Quantum Process Tomography of Non-Unitaries

by Shichuan Xue, Yizhi Wang, Yong Liu, Weixu Shi and Junjie Wu

Entropy 2023, 25(1), 90; https://doi.org/10.3390/e25010090 - 1 Jan 2023

Viewed by 1739

Abstract

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of [...] Read more.

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits (

d \leq 8

), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 855 KiB

Open AccessArticle

A Convex Hull-Based Machine Learning Algorithm for Multipartite Entanglement Classification

by Pingxun Wang

Appl. Sci. 2022, 12(24), 12778; https://doi.org/10.3390/app122412778 - 13 Dec 2022

Viewed by 1492

Abstract

Quantum entanglement becomes more complicated and capricious when more than two parties are involved. There have been methods for classifying some inequivalent multipartite entanglements, such as GHZ states and W states. In this paper, based on the fact that the set of all [...] Read more.

Quantum entanglement becomes more complicated and capricious when more than two parties are involved. There have been methods for classifying some inequivalent multipartite entanglements, such as GHZ states and W states. In this paper, based on the fact that the set of all W states is convex, we approximate the convex hull by some critical points from the inside and propose a method of classification via the tangent hyperplane. To accelerate the calculation, we bring ensemble learning of machine learning into the algorithm, thus improving the accuracy of the classification. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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16 pages, 596 KiB

Open AccessArticle

A Secured Half-Duplex Bidirectional Quantum Key Distribution Protocol against Collective Attacks

by Manal Khawasik, Wagdy Gomaa El-Sayed, M. Z. Rashad and Ahmed Younes

Symmetry 2022, 14(12), 2481; https://doi.org/10.3390/sym14122481 - 23 Nov 2022

Cited by 7 | Viewed by 2420

Abstract

Quantum Key Distribution is a secure method that implements cryptographic protocols. The applications of quantum key distribution technology have an important role: to enhance the security in communication systems. It is originally inspired by the physical concepts associated with quantum mechanics. It aims [...] Read more.

Quantum Key Distribution is a secure method that implements cryptographic protocols. The applications of quantum key distribution technology have an important role: to enhance the security in communication systems. It is originally inspired by the physical concepts associated with quantum mechanics. It aims to enable a secure exchange of cryptographic keys between two parties through an unsecured quantum communication channel. This work proposes a secure half-duplex bidirectional quantum key distribution protocol. The security of the proposed protocol is proved against collective attacks by estimating the interception of any eavesdropper with high probability in both directions under the control of the two parties. A two-qubit state encodes two pieces of information; the first qubit represents the transmitted bit and the second qubit represents the basis used for measurement. The partial diffusion operator is used to encrypt the transmitted qubit state as an extra layer of security. The predefined symmetry transformations induced by unitary in conjunction with the asymmetrical two-qubit teleportation scheme retain the protocol’s secrecy. Compared to the previous protocols, the proposed protocol has better performance on qubit efficiency. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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10 pages, 261 KiB

Open AccessArticle

Two Quantum Proxy Blind Signature Schemes Based on Controlled Quantum Teleportation

by Qiming Luo, Tinggui Zhang, Xiaofen Huang and Naihuan Jing

Entropy 2022, 24(10), 1421; https://doi.org/10.3390/e24101421 - 5 Oct 2022

Cited by 4 | Viewed by 1481

Abstract

We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted [...] Read more.

We present a scheme for teleporting an unknown, two-particle entangled state with a message from a sender (Alice) to a receiver (Bob) via a six-particle entangled channel. We also present another scheme for teleporting an unknown one-particle entangled state with a message transmitted in a two-way form between the same sender and receiver via a five-qubit cluster state. One-way hash functions, Bell-state measurements, and unitary operations are adopted in these two schemes. Our schemes use the physical characteristics of quantum mechanics to implement delegation, signature, and verification processes. Moreover, a quantum key distribution protocol and a one-time pad are adopted in these schemes. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

17 pages, 322 KiB

Open AccessArticle

Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians

by Maurice de Gosson and Charlyne de Gosson

Symmetry 2022, 14(9), 1890; https://doi.org/10.3390/sym14091890 - 9 Sep 2022

Cited by 3 | Viewed by 1637

Abstract

We apply the notion of polar duality from convex geometry to the study of quantum covariance ellipsoids in symplectic phase space. We consider in particular the case of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of [...] Read more.

We apply the notion of polar duality from convex geometry to the study of quantum covariance ellipsoids in symplectic phase space. We consider in particular the case of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle in its strong Robertson–Schrödinger form. We show that these phase space units can be characterized by a simple condition of reflexivity using polar duality, thus improving previous results. We apply these geometric constructions to the characterization of pure Gaussian states in terms of partial information on the covariance ellipsoid, which allows us to formulate statements related to symplectic tomography. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

12 pages, 2301 KiB

Open AccessArticle

Four-Qubit Cluster States Generation through Multi-Coin Quantum Walk

by Tianyi Wang, Xiaoguang Chen and Jianxiong Liang

Appl. Sci. 2022, 12(17), 8750; https://doi.org/10.3390/app12178750 - 31 Aug 2022

Viewed by 1843

Abstract

Quantum computing requires large numbers of resources of entangled qubits, which cannot be satisfied using traditional methods of entanglement generation, such as optical systems. Therefore, we need more efficient ways of entanglement generation. It has been proved that multi-coin quantum walks can be [...] Read more.

Quantum computing requires large numbers of resources of entangled qubits, which cannot be satisfied using traditional methods of entanglement generation, such as optical systems. Therefore, we need more efficient ways of entanglement generation. It has been proved that multi-coin quantum walks can be used to replace direct Bell state measurements during the process of entanglement generation in order to avoid the difficulty of Bell state measurement. In this paper, we take one step further and generate 4-qubit cluster states using multi-coin quantum walks, which simplifies the generation of 4-qubit cluster states by using only Bell states and local measurements. We also propose a method for preparing 4-qubit cluster states with quantum circuits to facilitate their use in quantum computing. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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14 pages, 485 KiB

Open AccessArticle

High-Speed Privacy Amplification Algorithm Using Cellular Automate in Quantum Key Distribution

by Yekai Lu, Enjian Bai, Xue-qin Jiang and Yun Wu

Electronics 2022, 11(15), 2426; https://doi.org/10.3390/electronics11152426 - 4 Aug 2022

Cited by 2 | Viewed by 1853

Abstract

Privacy amplification is an important step in the post-processing of quantum communication, which plays an indispensable role in the security of quantum key distribution systems. In this paper, we propose a Cellular Automata-based privacy amplification algorithm, which improves the speed of key distribution. [...] Read more.

Privacy amplification is an important step in the post-processing of quantum communication, which plays an indispensable role in the security of quantum key distribution systems. In this paper, we propose a Cellular Automata-based privacy amplification algorithm, which improves the speed of key distribution. The proposed algorithm is characterized by block iteration to generate secure key of arbitrary length. The core of the algorithm in this paper is to use the property that Cellular Automata can generate multiple new associated random sequences at the same time to carry out bit operations for multiple negotiation keys in the meantime and calculate in turn, so as to quickly realize the compression of negotiation keys. By analyzing the final key, the proposed algorithm has the advantages of fast key generation speed and high real-time performance. At the same time, the results of the NIST randomness test and avalanche test show that the algorithm has good randomness performance. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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20 pages, 412 KiB

Open AccessArticle

Group Actions and Monotone Quantum Metric Tensors

by Florio Maria Ciaglia and Fabio Di Nocera

Mathematics 2022, 10(15), 2613; https://doi.org/10.3390/math10152613 - 26 Jul 2022

Cited by 2 | Viewed by 1280

Abstract

The interplay between actions of Lie groups and monotone quantum metric tensors on the space of faithful quantum states of a finite-level system observed in recent works is here further developed. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

9 pages, 1929 KiB

Open AccessArticle

Experimental Demonstration of an Efficient Mach–Zehnder Modulator Bias Control for Quantum Key Distribution Systems

by Chang-Hoon Park, Min-Ki Woo, Byung-Kwon Park, Seung-Woo Jeon, Hojoong Jung, Sangin Kim and Sang-Wook Han

Electronics 2022, 11(14), 2207; https://doi.org/10.3390/electronics11142207 - 14 Jul 2022

Cited by 2 | Viewed by 2845

Abstract

A Mach–Zehnder modulator (MZM) is necessary for implementing a decoy-state protocol in a practical quantum key distribution (QKD) system. However, an MZM bias control method optimized for QKD systems has been missing to date. In this study, we propose an MZM bias control [...] Read more.

A Mach–Zehnder modulator (MZM) is necessary for implementing a decoy-state protocol in a practical quantum key distribution (QKD) system. However, an MZM bias control method optimized for QKD systems has been missing to date. In this study, we propose an MZM bias control method using N (≥2) diagnostic pulses. The proposed method can be efficiently applied to a QKD system without any additional hardware such as light sources or detectors. Furthermore, it does not reduce the key rate significantly because it uses time slots allocated to existing decoy pulses. We conducted an experimental demonstration of the proposed method in a field-deployed 1 × 3 QKD network and a laboratory test. It is shown that our method can maintain the MZM extinction ratio stably over 20 dB (bit error rate ≤1%), even in an actual network environment for a significant period. Consequently, we achieved successful QKD performances. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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9 pages, 3058 KiB

Open AccessArticle

Generation of Decoy Signals Using Optical Amplifiers for a Plug-and-Play Quantum Key Distribution System

by Min-Ki Woo, Chang-Hoon Park, Sangin Kim and Sang-Wook Han

Appl. Sci. 2022, 12(13), 6491; https://doi.org/10.3390/app12136491 - 27 Jun 2022

Cited by 2 | Viewed by 2263

Abstract

In most quantum key distribution (QKD) systems, a decoy-state protocol is implemented for preventing potential quantum attacks and higher mean photon rates. An optical intensity modulator attenuating the signal intensity is used to implement it in a QKD system adopting a one-way architecture. [...] Read more.

In most quantum key distribution (QKD) systems, a decoy-state protocol is implemented for preventing potential quantum attacks and higher mean photon rates. An optical intensity modulator attenuating the signal intensity is used to implement it in a QKD system adopting a one-way architecture. However, in the case of the plug-and-play (or two-way) architecture, there are technical issues, including random polarization of the input signal pulse and long-term stability. In this study, we propose a method for generating decoy pulses through amplification using an optical amplifier. The proposed scheme operates regardless of the input signal polarization. In addition, a circulator was added to adjust the signal intensity when the signal enters the input and exits the QKD transmitter by monitoring the intensity of the output signal pulse. It also helps to defend against Trojan horse attacks. A test setup for the proof-of-principle experiment was implemented and tested, and it was shown that the system operated stably with a quantum bit error rate (QBER) value of less than 5% over 26 h using a quantum channel (QC) of 25 km. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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9 pages, 642 KiB

Open AccessArticle

Comparison of Lumped Oscillator Model and Energy Participation Ratio Methods in Designing Two-Dimensional Superconducting Quantum Chips

by Benzheng Yuan, Weilong Wang, Fudong Liu, Haoran He and Zheng Shan

Entropy 2022, 24(6), 792; https://doi.org/10.3390/e24060792 - 7 Jun 2022

Cited by 4 | Viewed by 3190

Abstract

Over the past two decades, superconducting quantum circuits have become one of the essential platforms for realizing quantum computers. The Hamiltonian of a superconducting quantum circuit system is the key to describing the dynamic evolution of the system. For this reason, various methods [...] Read more.

Over the past two decades, superconducting quantum circuits have become one of the essential platforms for realizing quantum computers. The Hamiltonian of a superconducting quantum circuit system is the key to describing the dynamic evolution of the system. For this reason, various methods for analyzing the Hamiltonian of a superconducting quantum circuit system have been proposed, among which the LOM (Lumped Oscillator Model) and the EPR (Energy Participation Ratio) methods are the most popular ones. To analyze and improve the design methods of superconducting quantum chips, this paper compares the similarities and differences of the LOM and the EPR quantification methods. We verify the applicability of these two theoretical approaches to the design of 2D transmon quantum chips. By comparing the theoretically simulated results and the experimentally measured data at extremely low temperature, the errors between the theoretical calculation and observed measurement values of the two methods were summarized. Results show that the LOM method has more parameter outputs in data diversity and the qubit frequency calculation in LOM is more accurate. The reason is that in LOM more coupling between different systems are taken into consideration. These analyses would have reference significance for the design of superconducting quantum chips. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 488 KiB

Open AccessArticle

Using a Deep Quantum Neural Network to Enhance the Fidelity of Quantum Convolutional Codes

by Hanwei Xiao, Xiaoguang Chen and Jin Xu

Appl. Sci. 2022, 12(11), 5662; https://doi.org/10.3390/app12115662 - 2 Jun 2022

Cited by 3 | Viewed by 1644

Abstract

The fidelity of quantum states is an important concept in quantum information. Improving quantum fidelity is very important for both quantum communication and quantum computation. In this paper, we use a quantum neural network (QNN) to enhance the fidelity of [6, 2, 2] [...] Read more.

The fidelity of quantum states is an important concept in quantum information. Improving quantum fidelity is very important for both quantum communication and quantum computation. In this paper, we use a quantum neural network (QNN) to enhance the fidelity of [6, 2, 2] quantum convolutional codes. Towards the circuit of quantum convolutional codes, the target quantum state

| 0 ⟩

or

| 1 ⟩

is turned into entangled quantum states, which can defend against quantum noise more effectively. As the quantum neural network works better for quantum states with low dimension, we divide the quantum circuits into two parts. Then we apply the quantum neural network to each part of the circuit. The results of the simulation show that the network performs well in enhancing the fidelity of the quantum states. Through the quantum neural network, the fidelity of the first part is enhanced from

95.2 %

to

99.99 %

, and the fidelity of the second part is enhanced from

93.88 %

to

94.57 %

. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 308 KiB

Open AccessFeature PaperArticle

Gull’s Theorem Revisited

by Richard D. Gill

Entropy 2022, 24(5), 679; https://doi.org/10.3390/e24050679 - 11 May 2022

Cited by 4 | Viewed by 5299

Abstract

In 2016, Steve Gull has outlined has outlined a proof of Bell’s theorem using Fourier theory. Gull’s philosophy is that Bell’s theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing [...] Read more.

In 2016, Steve Gull has outlined has outlined a proof of Bell’s theorem using Fourier theory. Gull’s philosophy is that Bell’s theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell’s work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob’s computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull’s proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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10 pages, 4454 KiB

Open AccessArticle

Finite-Key Analysis of 1-Decoy Method Quantum Key Distribution with Intensity Fluctuation

by Chun Zhou, Yu Zhou, Yangbin Xu, Yang Wang, Yifei Lu, Musheng Jiang, Xiaoxu Zhang and Wansu Bao

Appl. Sci. 2022, 12(9), 4709; https://doi.org/10.3390/app12094709 - 7 May 2022

Viewed by 1539

Abstract

The decoy state quantum key distribution (QKD) protocol is proven to be an effective strategy against the photon number splitting attack. It was shown that the 1-decoy state protocol, easier to implement in the practical QKD system, outperforms the 2-decoy state protocol for [...] Read more.

The decoy state quantum key distribution (QKD) protocol is proven to be an effective strategy against the photon number splitting attack. It was shown that the 1-decoy state protocol, easier to implement in the practical QKD system, outperforms the 2-decoy state protocol for block sizes of up to

10^{8}

bits. How intensity fluctuations influence the performance of the 1-decoy state protocol with finite resources remains a pending issue. In this paper, we present a finite-key analysis of the 1-decoy state protocol with intensity fluctuations and obtain the secret key rate formula about intensity fluctuations. Our numerical simulation results show that the stronger the intensity fluctuations, the lower the secret key rate for a small data block size of a few bits. Our research can provide theoretical implications for the selection of data size in the QKD system with intensity fluctuations. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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17 pages, 624 KiB

Open AccessArticle

Quantum-Inspired Complex-Valued Language Models for Aspect-Based Sentiment Classification

by Qin Zhao, Chenguang Hou and Ruifeng Xu

Entropy 2022, 24(5), 621; https://doi.org/10.3390/e24050621 - 29 Apr 2022

Cited by 2 | Viewed by 2349

Abstract

Aiming at classifying the polarities over aspects, aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. The vector representations of current models are generally constrained to real values. Based on mathematical formulations of quantum theory, quantum language models have drawn increasing [...] Read more.

Aiming at classifying the polarities over aspects, aspect-based sentiment analysis (ABSA) is a fine-grained task of sentiment analysis. The vector representations of current models are generally constrained to real values. Based on mathematical formulations of quantum theory, quantum language models have drawn increasing attention. Words in such models can be projected as physical particles in quantum systems, and naturally represented by representation-rich complex-valued vectors in a Hilbert Space, rather than real-valued ones. In this paper, the Hilbert Space representation for ABSA models is investigated and the complexification of three strong real-valued baselines are constructed. Experimental results demonstrate the effectiveness of complexification and the outperformance of our complex-valued models, illustrating that the complex-valued embedding can carry additional information beyond the real embedding. Especially, a complex-valued RoBERTa model outperforms or approaches the previous state-of-the-art on three standard benchmarking datasets. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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14 pages, 829 KiB

Open AccessArticle

Measurement Uncertainty, Purity, and Entanglement Dynamics of Maximally Entangled Two Qubits Interacting Spatially with Isolated Cavities: Intrinsic Decoherence Effect

by Abdel-Baset A. Mohamed, Atta Ur Rahman and Hichem Eleuch

Entropy 2022, 24(4), 545; https://doi.org/10.3390/e24040545 - 13 Apr 2022

Cited by 12 | Viewed by 2145

Abstract

In a system of two charge-qubits that are initially prepared in a maximally entangled Bell’s state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even [...] Read more.

In a system of two charge-qubits that are initially prepared in a maximally entangled Bell’s state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even coherent cavity fields. For different initial cavity configurations, the temporal evolution of the final state of qubits and cavities is solved analytically. The effects of intrinsic decoherence and detuning strength on the dynamics of bipartite entropic uncertainty, purity and entanglement are explored. Depending on the field parameters, nonclassical correlations can be preserved. Nonclassical correlations and revival aspects appear to be significantly inhibited when intrinsic decoherence increases. Nonclassical correlations stay longer and have greater revivals due to the high detuning of the two qubits and the coherence strength of the initial cavity fields. Quantum memory-assisted entropic uncertainty and entropy have similar dynamics while the negativity presents fewer revivals in contrast. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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25 pages, 561 KiB

Open AccessArticle

An Information Quantity in Pure State Models

by Fuyuhiko Tanaka

Entropy 2022, 24(4), 541; https://doi.org/10.3390/e24040541 - 12 Apr 2022

Viewed by 1944

Abstract

When we consider an error model in a quantum computing system, we assume a parametric model where a prepared qubit belongs. Keeping this in mind, we focus on the evaluation of the amount of information we obtain when we know the system belongs [...] Read more.

When we consider an error model in a quantum computing system, we assume a parametric model where a prepared qubit belongs. Keeping this in mind, we focus on the evaluation of the amount of information we obtain when we know the system belongs to the model within the parameter range. Excluding classical fluctuations, uncertainty still remains in the system. We propose an information quantity called purely quantum information to evaluate this and give it an operational meaning. For the qubit case, it is relevant to the facility location problem on the unit sphere, which is well known in operations research. For general cases, we extend this to the facility location problem in complex projective spaces. Purely quantum information reflects the uncertainty of a quantum system and is related to the minimum entropy rather than the von Neumann entropy. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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31 pages, 2753 KiB

Open AccessArticle

Shared Quantum Key Distribution Based on Asymmetric Double Quantum Teleportation

by Carlos Cardoso-Isidoro and Francisco Delgado

Symmetry 2022, 14(4), 713; https://doi.org/10.3390/sym14040713 - 1 Apr 2022

Cited by 9 | Viewed by 2834

Abstract

Quantum cryptography is a well-stated field within quantum applications where quantum information is used to set secure communications, authentication, and secret keys. Now used in quantum devices with those purposes, particularly Quantum Key Distribution (QKD), which proposes a secret key between two parties [...] Read more.

Quantum cryptography is a well-stated field within quantum applications where quantum information is used to set secure communications, authentication, and secret keys. Now used in quantum devices with those purposes, particularly Quantum Key Distribution (QKD), which proposes a secret key between two parties free of effective eavesdropping, at least at a higher level than classical cryptography. The best-known quantum protocol to securely share a secret key is the BB84 one. Other protocols have been proposed as adaptations of it. Most of them are based on the quantum indeterminacy for non-orthogonal quantum states. Their security is commonly based on the large length of the key. In the current work, a BB84-like procedure for QKD based on double quantum teleportation allows the sharing of the key statement using several parties. Thus, the quantum bits of information are assembled among three parties via entanglement, instead of travelling through a unique quantum channel as in the traditional protocol. Asymmetry in the double teleportation plus post-measurement retains the secrecy in the process. Despite requiring more complex control and resources, the procedure dramatically reduces the probability of success for an eavesdropper under individual attacks, because of the ignorance of the processing times in the procedure. Quantum Bit Error Rate remains in the acceptable threshold and it becomes configurable. The article depicts the double quantum teleportation procedure, the associated control to introduce the QKD scheme, the analysis of individual attacks performed by an eavesdropper, and a brief comparison with other protocols. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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14 pages, 3369 KiB

Open AccessEditor’s ChoiceArticle

A Multi-Classification Hybrid Quantum Neural Network Using an All-Qubit Multi-Observable Measurement Strategy

by Yi Zeng, Hao Wang, Jin He, Qijun Huang and Sheng Chang

Entropy 2022, 24(3), 394; https://doi.org/10.3390/e24030394 - 11 Mar 2022

Cited by 21 | Viewed by 5470

Abstract

Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the [...] Read more.

Quantum machine learning is a promising application of quantum computing for data classification. However, most of the previous research focused on binary classification, and there are few studies on multi-classification. The major challenge comes from the limitations of near-term quantum devices on the number of qubits and the size of quantum circuits. In this paper, we propose a hybrid quantum neural network to implement multi-classification of a real-world dataset. We use an average pooling downsampling strategy to reduce the dimensionality of samples, and we design a ladder-like parameterized quantum circuit to disentangle the input states. Besides this, we adopt an all-qubit multi-observable measurement strategy to capture sufficient hidden information from the quantum system. The experimental results show that our algorithm outperforms the classical neural network and performs especially well on different multi-class datasets, which provides some enlightenment for the application of quantum computing to real-world data on near-term quantum processors. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 292 KiB

Open AccessArticle

Construction of a Family of Maximally Entangled Bases in ℂ^d ⊗ ℂ^d′

by Chenghong Wang, Kun Wang and Zhu-Jun Zheng

Entropy 2022, 24(3), 373; https://doi.org/10.3390/e24030373 - 6 Mar 2022

Cited by 1 | Viewed by 2013

Abstract

In this paper, we present a new method for the construction of maximally entangled states in

C^{d} \otimes C^{d^{'}}

when

d^{'} \geq 2 d

. A systematic way of constructing a set of maximally entangled bases (MEBs) in [...] Read more.

In this paper, we present a new method for the construction of maximally entangled states in

C^{d} \otimes C^{d^{'}}

when

d^{'} \geq 2 d

. A systematic way of constructing a set of maximally entangled bases (MEBs) in

C^{d} \otimes C^{d^{'}}

was established. Both cases when

d^{'}

is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in

C^{2} \otimes C^{4}

, which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in

C^{2} \otimes C^{5}

. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

10 pages, 229 KiB

Open AccessArticle

Quantum Attacks on Sum of Even–Mansour Construction with Linear Key Schedules

by Ping Zhang

Entropy 2022, 24(2), 153; https://doi.org/10.3390/e24020153 - 20 Jan 2022

Cited by 5 | Viewed by 2459

Abstract

Shinagawa and Iwata are considered quantum security for the sum of Even–Mansour (SoEM) construction and provided quantum key recovery attacks by Simon’s algorithm and Grover’s algorithm. Furthermore, quantum key recovery attacks are also presented for natural generalizations of SoEM. For some variants of [...] Read more.

Shinagawa and Iwata are considered quantum security for the sum of Even–Mansour (SoEM) construction and provided quantum key recovery attacks by Simon’s algorithm and Grover’s algorithm. Furthermore, quantum key recovery attacks are also presented for natural generalizations of SoEM. For some variants of SoEM, they found that their quantum attacks are not obvious and left it as an open problem to discuss the security of such constructions. This paper focuses on this open problem and presents a positive response. We provide quantum key recovery attacks against such constructions by quantum algorithms. For natural generalizations of SoEM with linear key schedules, we also present similar quantum key recovery attacks by quantum algorithms (Simon’s algorithm, Grover’s algorithm, and Grover-meet-Simon algorithm). Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

13 pages, 1454 KiB

Open AccessArticle

Security Analysis of Continuous-Variable Measurement-Device-Independent Quantum Key Distribution Systems in Complex Communication Environments

by Yi Zheng, Haobin Shi, Wei Pan, Quantao Wang and Jiahui Mao

Entropy 2022, 24(1), 127; https://doi.org/10.3390/e24010127 - 14 Jan 2022

Cited by 4 | Viewed by 2220

Abstract

Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here [...] Read more.

Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 3013 KiB

Open AccessArticle

Percolation Distribution in Small-World Quantum Networks

by Jianxiong Liang, Xiaoguang Chen and Tianyi Wang

Appl. Sci. 2022, 12(2), 701; https://doi.org/10.3390/app12020701 - 11 Jan 2022

Viewed by 1658

Abstract

Quantum networks have good prospects for applications in the future. Compared with classical networks, small-world quantum networks have some interesting properties. The topology of the network can be changed through entanglement exchange operations, and different network topologies will result in different percolation thresholds [...] Read more.

Quantum networks have good prospects for applications in the future. Compared with classical networks, small-world quantum networks have some interesting properties. The topology of the network can be changed through entanglement exchange operations, and different network topologies will result in different percolation thresholds when performing entanglement percolation. A lower percolation threshold means that quantum networks require fewer minimum resources for communication. Since a shared singlet between two nodes can still be a limitation, concurrency percolation theory (ConPT) can be used to relax the condition. In this paper, we investigate how entanglement distribution is performed in small-world quantum networks to ensure that nodes in the network can communicate with each other by establishing communication links through entanglement swapping. Any node can perform entanglement swapping on only part of the connected edges, which can reduce the influence of each node in the network during entanglement swapping. In addition, the ConPT method is used to reduce the percolation threshold even further, thus obtaining a better network structure and reducing the resources required. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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10 pages, 272 KiB

Open AccessArticle

Steering Witness and Steering Criterion of Gaussian States

by Ruifen Ma, Taotao Yan, Dantong Wu and Xiaofei Qi

Entropy 2022, 24(1), 62; https://doi.org/10.3390/e24010062 - 29 Dec 2021

Cited by 2 | Viewed by 1653

Abstract

Quantum steering is an important quantum resource, which is intermediate between entanglement and Bell nonlocality. In this paper, we study steering witnesses for Gaussian states in continuous-variable systems. We give a definition of steering witnesses by covariance matrices of Gaussian states, and then [...] Read more.

Quantum steering is an important quantum resource, which is intermediate between entanglement and Bell nonlocality. In this paper, we study steering witnesses for Gaussian states in continuous-variable systems. We give a definition of steering witnesses by covariance matrices of Gaussian states, and then obtain a steering criterion by steering witnesses to detect steerability of any

(m + n)

-mode Gaussian states. In addition, the conditions for two steering witnesses to be comparable and the optimality of steering witnesses are also discussed. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

23 pages, 2705 KiB

Open AccessArticle

Many-Objective Quantum-Inspired Particle Swarm Optimization Algorithm for Placement of Virtual Machines in Smart Computing Cloud

by Jerzy Balicki

Entropy 2022, 24(1), 58; https://doi.org/10.3390/e24010058 - 28 Dec 2021

Cited by 11 | Viewed by 4245

Abstract

Particle swarm optimization algorithm (PSO) is an effective metaheuristic that can determine Pareto-optimal solutions. We propose an extended PSO by introducing quantum gates in order to ensure the diversity of particle populations that are looking for efficient alternatives. The quality of solutions was [...] Read more.

Particle swarm optimization algorithm (PSO) is an effective metaheuristic that can determine Pareto-optimal solutions. We propose an extended PSO by introducing quantum gates in order to ensure the diversity of particle populations that are looking for efficient alternatives. The quality of solutions was verified in the issue of assignment of resources in the computing cloud to improve the live migration of virtual machines. We consider the multi-criteria optimization problem of deep learning-based models embedded into virtual machines. Computing clouds with deep learning agents can support several areas of education, smart city or economy. Because deep learning agents require lots of computer resources, seven criteria are studied such as electric power of hosts, reliability of cloud, CPU workload of the bottleneck host, communication capacity of the critical node, a free RAM capacity of the most loaded memory, a free disc memory capacity of the most busy storage, and overall computer costs. Quantum gates modify an accepted position for the current location of a particle. To verify the above concept, various simulations have been carried out on the laboratory cloud based on the OpenStack platform. Numerical experiments have confirmed that multi-objective quantum-inspired particle swarm optimization algorithm provides better solutions than the other metaheuristics. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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19 pages, 571 KiB

Open AccessArticle

Unambiguous State Discrimination with Intrinsic Coherence

by Jin-Hua Zhang, Fu-Lin Zhang, Zhi-Xi Wang, Hui Yang and Shao-Ming Fei

Entropy 2022, 24(1), 18; https://doi.org/10.3390/e24010018 - 23 Dec 2021

Cited by 2 | Viewed by 2569

Abstract

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, [...] Read more.

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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14 pages, 408 KiB

Open AccessArticle

Error Probability Mitigation in Quantum Reading Using Classical Codes

by Francisco Revson Fernandes Pereira and Stefano Mancini

Entropy 2022, 24(1), 5; https://doi.org/10.3390/e24010005 - 21 Dec 2021

Cited by 1 | Viewed by 2551

Abstract

A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes [...] Read more.

A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed–Solomon codes, BCH codes, and Reed–Muller codes. In conjunction with the use of codes, we also analyze the role of the receiver. In particular, heterodyne and Dolinar receivers are taken into consideration. The encoding and measurement schemes are connected by the probing step. As probes, we consider coherent states. In such a simple manner, interesting results are obtained. As we show, there is a threshold below which using codes surpass optimal and sophisticated schemes for any fixed rate and code. BCH codes in conjunction with Dolinar receiver turn out to be the optimal strategy for error mitigation in quantum reading. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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11 pages, 567 KiB

Open AccessArticle

Robust Quantum Search with Uncertain Number of Target States

by Yuanye Zhu, Zeguo Wang, Bao Yan and Shijie Wei

Entropy 2021, 23(12), 1649; https://doi.org/10.3390/e23121649 - 8 Dec 2021

Cited by 4 | Viewed by 2759

Abstract

The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked [...] Read more.

The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given

λ = \sqrt{M / N}

, where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity

O (\sqrt{N})

as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio

M / N

. In particular, for a database with an uncertainty in the ratio

\frac{M \pm \sqrt{M}}{N}

, our algorithm will find the target states with a success rate no less than

96 %

. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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12 pages, 429 KiB

Open AccessArticle

The Tightness of Multipartite Coherence from Spectrum Estimation

by Qi-Ming Ding, Xiao-Xu Fang and He Lu

Entropy 2021, 23(11), 1519; https://doi.org/10.3390/e23111519 - 15 Nov 2021

Cited by 6 | Viewed by 1902

Abstract

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is [...] Read more.

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, the

l_{1}

-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing)

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