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281 KiB

Open AccessArticle

Fluctuations of Intensive Quantities in Statistical Thermodynamics

by Artur E. Ruuge

Entropy 2013, 15(11), 4889-4908; https://doi.org/10.3390/e15114889 - 11 Nov 2013

Cited by 2 | Viewed by 4732

In phenomenological thermodynamics, the canonical coordinates of a physical system split in pairs, with each pair consisting of an extensive quantity and an intensive one. In the present paper, the quasithermodynamic fluctuation theory of a model system of a large number of oscillators [...] Read more.

In phenomenological thermodynamics, the canonical coordinates of a physical system split in pairs, with each pair consisting of an extensive quantity and an intensive one. In the present paper, the quasithermodynamic fluctuation theory of a model system of a large number of oscillators is extended to statistical thermodynamics based on the idea of perceiving the fluctuations of intensive variables as the fluctuations of specific extensive ones in a “thermodynamically dual” system. The extension is motivated by the symmetry of the problem in the context of an analogy with quantum mechanics, which is stated in terms of a generalized Pauli problem for the thermodynamic fluctuations. The doubled Boltzmann constant divided by the number of particles plays a similar role as the Planck constant. Full article

(This article belongs to the Special Issue Quantum Information 2012)

247 KiB

Open AccessArticle

Dynamic Distance Measure on Spaces of Isospectral Mixed Quantum States

by Ole Andersson and Hoshang Heydari

Entropy 2013, 15(9), 3688-3697; https://doi.org/10.3390/e15093688 - 06 Sep 2013

Cited by 9 | Viewed by 4374

Abstract

Distance measures are used to quantify the extent to which information is preserved or altered by quantum processes, and thus are indispensable tools in quantum information and quantum computing. In this paper we propose a new distance measure for mixed quantum states, which [...] Read more.

Distance measures are used to quantify the extent to which information is preserved or altered by quantum processes, and thus are indispensable tools in quantum information and quantum computing. In this paper we propose a new distance measure for mixed quantum states, which we call the dynamic distance measure, and we show that it is a proper distance measure. The dynamic distance measure is defined in terms of a measurable quantity, which makes it suitable for applications. In a final section we compare the dynamic distance measure with the well-known Bures distance measure. Full article

(This article belongs to the Special Issue Quantum Information 2012)

440 KiB

Open AccessArticle

Communicating through Probabilities: Does Quantum Theory Optimize the Transfer of Information?

by William K. Wootters

Entropy 2013, 15(8), 3130-3147; https://doi.org/10.3390/e15083220 - 02 Aug 2013

Cited by 9 | Viewed by 5022

Abstract

A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating [...] Read more.

A quantum measurement can be regarded as a communication channel, in which the parameters of the state are expressed only in the probabilities of the outcomes of the measurement. We begin this paper by considering, in a non-quantum-mechanical setting, the problem of communicating through probabilities. For example, a sender, Alice, wants to convey to a receiver, Bob, the value of a continuous variable, θ, but her only means of conveying this value is by sending Bob a coin in which the value of θ is encoded in the probability of heads. We ask what the optimal encoding is when Bob will be allowed to flip the coin only a finite number of times. As the number of tosses goes to infinity, we find that the optimal encoding is the same as what nature would do if we lived in a world governed by real-vector-space quantum theory. We then ask whether the problem might be modified, so that the optimal communication strategy would be consistent with standard, complex-vector-space quantum theory. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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468 KiB

Open AccessArticle

Quantum Contextuality with Stabilizer States

by Mark Howard, Eoin Brennan and Jiri Vala

Entropy 2013, 15(6), 2340-2362; https://doi.org/10.3390/e15062340 - 07 Jun 2013

Cited by 19 | Viewed by 7558

Abstract

The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error correcting codes—stabilizer codes—are built using Pauli operators. The eigenstates of these [...] Read more.

The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error correcting codes—stabilizer codes—are built using Pauli operators. The eigenstates of these operators—stabilizer states—display a structure (e.g., mutual orthogonality relationships) that has made them useful in examples of multi-qubit non-locality and contextuality. Here, we apply the graph-theoretical contextuality formalism of Cabello, Severini and Winter to sets of stabilizer states, with particular attention to the effect of generalizing two-level qubit systems to odd prime d-level qudit systems. While state-independent contextuality using two-qubit states does not generalize to qudits, we show explicitly how state-dependent contextuality associated with a Bell inequality does generalize. Along the way we note various structural properties of stabilizer states, with respect to their orthogonality relationships, which may be of independent interest. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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1013 KiB

Open AccessArticle

Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control

by Paul Watts, Maurice O'Connor and Jiří Vala

Entropy 2013, 15(6), 1963-1984; https://doi.org/10.3390/e15061963 - 23 May 2013

Cited by 19 | Viewed by 6458

Abstract

We derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we compute the invariant volume of the space of two-qubit [...] Read more.

We derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we compute the invariant volume of the space of two-qubit perfect entanglers. We find that this volume corresponds to more than 84% of the total invariant volume of the space of two-qubit gates. This same metric is also used to determine the effective target sizes that selected gates will present in any quantum-control procedure designed to implement them. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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2075 KiB

Open AccessArticle

Genuine Tripartite Entanglement and Nonlocality in Bose-Einstein Condensates by Collective Atomic Recoil

by Samanta Piano and Gerardo Adesso

Entropy 2013, 15(5), 1875-1886; https://doi.org/10.3390/e15051875 - 17 May 2013

Cited by 5 | Viewed by 6171

Abstract

We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper [...] Read more.

We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in any reduced two-mode bipartition. We further show that the state of the system exhibits genuine tripartite nonlocality, which can be revealed by a robust violation of the Svetlichny inequality when performing displaced parity measurements. Our exact results are obtained by exploiting the powerful machinery of phase-space informational measures for Gaussian states, which we briefly review in the opening sections of the paper. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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1471 KiB

Open AccessArticle

Entanglement Structure in Expanding Universes

by Yasusada Nambu

Entropy 2013, 15(5), 1847-1874; https://doi.org/10.3390/e15051847 - 16 May 2013

Cited by 33 | Viewed by 5324

Abstract

We investigate entanglement of a quantum field in de Sitter spacetime using a particle detector model. By considering the entanglement between two comoving detectors interacting with a scalar field, it is possible to detect the entanglement of the scalar field by swapping it [...] Read more.

We investigate entanglement of a quantum field in de Sitter spacetime using a particle detector model. By considering the entanglement between two comoving detectors interacting with a scalar field, it is possible to detect the entanglement of the scalar field by swapping it to detectors. For the massless minimal scalar field, we find that the entanglement between the detectors cannot be detected when their physical separation exceeds the Hubble horizon scale. This behavior supports the appearance of the classical nature of quantum fluctuations generated during the inflationary era. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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239 KiB

Open AccessArticle

Equiangular Vectors Approach to Mutually Unbiased Bases

by Maurice R. Kibler

Entropy 2013, 15(5), 1726-1737; https://doi.org/10.3390/e15051726 - 08 May 2013

Cited by 3 | Viewed by 4898

Abstract

Two orthonormal bases in the d-dimensional Hilbert space are said to be unbiased if the square modulus of the inner product of any vector of one basis with any vector of the other equals 1 d. The presence of a modulus in the [...] Read more.

Two orthonormal bases in the d-dimensional Hilbert space are said to be unbiased if the square modulus of the inner product of any vector of one basis with any vector of the other equals 1 d. The presence of a modulus in the problem of finding a set of mutually unbiased bases constitutes a source of complications from the numerical point of view. Therefore, we may ask the question: Is it possible to get rid of the modulus? After a short review of various constructions of mutually unbiased bases in Cd, we show how to transform the problem of finding d + 1 mutually unbiased bases in the d-dimensional space Cd (with a modulus for the inner product) into the one of finding d(d+1) vectors in the d2-dimensional space Cd2 (without a modulus for the inner product). The transformation from Cd to Cd2 corresponds to the passage from equiangular lines to equiangular vectors. The transformation formulas are discussed in the case where d is a prime number. Full article

(This article belongs to the Special Issue Quantum Information 2012)

610 KiB

Open AccessArticle

All-Optically Controlled Quantum Memory for Light with a Cavity-Optomechanical System

by Jinjin Li, Wen Bin and Ka-Di Zhu

Entropy 2013, 15(2), 434-444; https://doi.org/10.3390/e15020434 - 24 Jan 2013

Cited by 5 | Viewed by 7867

Abstract

Optomechanics may be viewed as a light-mechanics interface to realize hybrid structures for (classical or quantum) information processing, switching or storage. Using the two-laser technique, in this paper, we theoretically devise a protocol for quantum light memory via a cavity optomechanical system composed [...] Read more.

Optomechanics may be viewed as a light-mechanics interface to realize hybrid structures for (classical or quantum) information processing, switching or storage. Using the two-laser technique, in this paper, we theoretically devise a protocol for quantum light memory via a cavity optomechanical system composed of a Fabry–Perot cavity and a mechanical resonator. Due to the long-lived mechanical resonator, this quantum memory for light based on optomechanically induced transparency (OMIT) can serve as a long-term memory that can store the full quantum light contained in an optical pulse. It is shown that, with the tunable pump laser, the quantum signal light can be reaccelerated and converted back on demand. Our presented work could open the door to all-optical routers for light memory devices and have a guide to actual experiments. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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Review

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3725 KiB

Open AccessReview

Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers

by Abdullah M. Iliyasu

Entropy 2013, 15(8), 2874-2974; https://doi.org/10.3390/e15082874 - 26 Jul 2013

Cited by 58 | Viewed by 9147

Abstract

Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images [...] Read more.

Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images and recovery of their unmarked versions on quantum computers are proposed. Encoding the images as 2ⁿ-sized normalised Flexible Representation of Quantum Images (FRQI) states, with n-qubits and 1-qubit dedicated to capturing the respective information about the colour and position of every pixel in the image respectively, the proposed algorithms utilise the flexibility inherent to the FRQI representation, in order to confine the transformations on an image to any predetermined chromatic or spatial (or a combination of both) content of the image as dictated by the watermark embedding, authentication or recovery circuits. Furthermore, by adopting an apt generalisation of the criteria required to realise physical quantum computing hardware, three standalone components that make up the framework to prepare, manipulate and recover the various contents required to represent and produce movies on quantum computers are also proposed. Each of the algorithms and the mathematical foundations for their execution were simulated using classical (i.e., conventional or non-quantum) computing resources, and their results were analysed alongside other longstanding classical computing equivalents. The work presented here, combined together with the extensions suggested, provide the basic foundations towards effectuating secure and efficient classical-like image and video processing applications on the quantum-computing framework. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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755 KiB

Open AccessReview

Quantum Thermodynamics: A Dynamical Viewpoint

by Ronnie Kosloff

Entropy 2013, 15(6), 2100-2128; https://doi.org/10.3390/e15062100 - 29 May 2013

Cited by 558 | Viewed by 30296

Abstract

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The [...] Read more.

Quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. The viewpoint advocated is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The emergence of the 0-law, I-law, II-law and III-law of thermodynamics from quantum considerations is presented. The emphasis is on consistency between the two theories, which address the same subject from different foundations. We claim that inconsistency is the result of faulty analysis, pointing to flaws in approximations. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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623 KiB

Open AccessReview

Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications

by Yu-Bo Sheng and Lan Zhou

Entropy 2013, 15(5), 1776-1820; https://doi.org/10.3390/e15051776 - 16 May 2013

Cited by 69 | Viewed by 8235

Abstract

Entanglement concentration is of most importance in long distance quantum communication and quantum computation. It is to distill maximally entangled states from pure partially entangled states based on the local operation and classical communication. In this review, we will mainly describe two kinds [...] Read more.

Entanglement concentration is of most importance in long distance quantum communication and quantum computation. It is to distill maximally entangled states from pure partially entangled states based on the local operation and classical communication. In this review, we will mainly describe two kinds of entanglement concentration protocols. One is to concentrate the partially entangled Bell-state, and the other is to concentrate the partially entangled W state. Some protocols are feasible in current experimental conditions and suitable for the optical, electric and quantum-dot and optical microcavity systems. Full article

(This article belongs to the Special Issue Quantum Information 2012)

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