Entropy

Research

Jump to: Other

14 pages, 737 KiB

Open AccessArticle

Analysis of Quantum Steering Measures

by Lucas Maquedano and Ana C. S. Costa

Entropy 2024, 26(3), 257; https://doi.org/10.3390/e26030257 - 14 Mar 2024

Viewed by 808

Abstract

The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to [...] Read more.

The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few approaches presented in order to measure the degree of steerability of a given system. In this work, we are interested in investigating possible ways to quantify quantum steering, where we based our analysis on different criteria presented in the literature. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

13 pages, 1384 KiB

Open AccessFeature PaperArticle

A Quantum Double-or-Nothing Game: An Application of the Kelly Criterion to Spins

by Bernhard K. Meister and Henry C. W. Price

Entropy 2024, 26(1), 66; https://doi.org/10.3390/e26010066 - 12 Jan 2024

Viewed by 890

Abstract

A quantum game is constructed from a sequence of independent and identically polarised spin-1/2 particles. Information about their possible polarisation is provided to a bettor, who can wager in successive double-or-nothing games on measurement outcomes. The choice at each stage is how much [...] Read more.

A quantum game is constructed from a sequence of independent and identically polarised spin-1/2 particles. Information about their possible polarisation is provided to a bettor, who can wager in successive double-or-nothing games on measurement outcomes. The choice at each stage is how much to bet and in which direction to measure the individual particles. The portfolio’s growth rate rises as the measurements are progressively adjusted in response to the accumulated information. Wealth is amassed through astute betting. The optimal classical strategy is called the Kelly criterion and plays a fundamental role in portfolio theory and consequently quantitative finance. The optimal quantum strategy is determined numerically and shown to differ from the classical strategy. This paper contributes to the development of quantum finance, as aspects of portfolio optimisation are extended to the quantum realm. Intriguing trade-offs between information gain and portfolio growth are described. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

33 pages, 4382 KiB

Open AccessFeature PaperArticle

Weak versus Deterministic Macroscopic Realism, and Einstein–Podolsky–Rosen’s Elements of Reality

by Jesse Fulton, Manushan Thenabadu, Run Yan Teh and Margaret D. Reid

Entropy 2024, 26(1), 11; https://doi.org/10.3390/e26010011 - 21 Dec 2023

Cited by 4 | Viewed by 980

Abstract

The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of [...] Read more.

The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

36 pages, 2377 KiB

Open AccessFeature PaperArticle

A Macroscopic Quantum Three-Box Paradox: Finding Consistency with Weak Macroscopic Realism

by Channa Hatharasinghe, Manushan Thenabadu, Peter D. Drummond and Margaret D. Reid

Entropy 2023, 25(12), 1620; https://doi.org/10.3390/e25121620 - 4 Dec 2023

Cited by 1 | Viewed by 931

Abstract

The quantum three-box paradox considers a ball prepared in a superposition of being in any one of three boxes. Bob makes measurements by opening either box 1 or box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the [...] Read more.

The quantum three-box paradox considers a ball prepared in a superposition of being in any one of three boxes. Bob makes measurements by opening either box 1 or box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening box 3. The paradox is that the ball would have been found with certainty by Bob in either box if that box had been opened. Resolutions of the paradox include that Bob’s measurement cannot be made non-invasively or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes prior to Bob or Alice opening any boxes. We demonstrate the consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any boxes but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: the paradox only manifests if Alice’s shuffling combines both local operations (on box 3) and nonlocal operations, on the other boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett–Garg inequality, which implies failure of non-invasive measurability if wMR holds. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

10 pages, 431 KiB

Open AccessArticle

Insecurity of Quantum Blockchains Based on Entanglement in Time

by Piotr Zawadzki

Entropy 2023, 25(9), 1344; https://doi.org/10.3390/e25091344 - 16 Sep 2023

Viewed by 808

Abstract

In this study, the security implications of utilizing the concept of entanglement in time in the quantum representation of a blockchain data structure are investigated. The analysis reveals that the fundamental idea underlying this representation relies on an uncertain interpretation of experimental results. [...] Read more.

In this study, the security implications of utilizing the concept of entanglement in time in the quantum representation of a blockchain data structure are investigated. The analysis reveals that the fundamental idea underlying this representation relies on an uncertain interpretation of experimental results. A different perspective is provided by adopting the Copenhagen interpretation, which explains the observed correlations in the experiment without invoking the concept of entanglement in time. According to this interpretation, the qubits responsible for these correlations are not entangled, posing a challenge to the security foundation of the data structure. The study incorporates theoretical analysis, numerical simulations, and experiments using real quantum hardware. By employing a dedicated circuit for detecting genuine entanglement, the existence of entanglement in the process of generating a quantum blockchain is conclusively excluded. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

21 pages, 465 KiB

Open AccessArticle

Generalized Bell Scenarios: Disturbing Consequences on Local-Hidden-Variable Models

by André Mazzari, Gabriel Ruffolo, Carlos Vieira, Tassius Temistocles, Rafael Rabelo and Marcelo Terra Cunha

Entropy 2023, 25(9), 1276; https://doi.org/10.3390/e25091276 - 30 Aug 2023

Viewed by 755

Abstract

Bell nonlocality and Kochen–Specker contextuality are among the main topics in the foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems, while the latter considers a single system. In recent works, [...] Read more.

Bell nonlocality and Kochen–Specker contextuality are among the main topics in the foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems, while the latter considers a single system. In recent works, a unified framework for these phenomena was presented. This article reviews, expands, and obtains new results regarding this framework. Contextual and disturbing features inside the local models are explored, which allows for the definition of different local sets with a non-trivial relation among them. The relations between the set of quantum correlations and these local sets are also considered, and post-quantum local behaviours are found. Moreover, examples of correlations that are both local and non-contextual but such that these two classical features cannot be expressed by the same hidden variable model are shown. Extensions of the Fine–Abramsky–Brandenburger theorem are also discussed. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

19 pages, 522 KiB

Open AccessFeature PaperArticle

Covariance-Matrix-Based Criteria for Network Entanglement

by Kiara Hansenne and Otfried Gühne

Entropy 2023, 25(9), 1260; https://doi.org/10.3390/e25091260 - 24 Aug 2023

Viewed by 752

Abstract

Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful [...] Read more.

Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

14 pages, 359 KiB

Open AccessFeature PaperArticle

Optimal Information Transfer and the Uniform Measure over Probability Space

by William K. Wootters

Entropy 2023, 25(6), 875; https://doi.org/10.3390/e25060875 - 30 May 2023

Viewed by 979

Abstract

For a quantum system with a d-dimensional Hilbert space, suppose a pure state

| ψ ⟩

is subjected to a complete orthogonal measurement. The measurement effectively maps

| ψ ⟩

to a point

(p_{1}, \dots, p_{d})

[...] Read more.

For a quantum system with a d-dimensional Hilbert space, suppose a pure state

| ψ ⟩

is subjected to a complete orthogonal measurement. The measurement effectively maps

| ψ ⟩

to a point

(p_{1}, \dots, p_{d})

in the appropriate probability simplex. It is a known fact—which depends crucially on the complex nature of the system’s Hilbert space—that if

| ψ ⟩

is distributed uniformly over the unit sphere, then the resulting ordered set

(p_{1}, \dots, p_{d})

is distributed uniformly over the probability simplex; that is, the resulting measure on the simplex is proportional to

d p_{1} \dots d p_{d - 1}

. In this paper we ask whether there is some foundational significance to this uniform measure. In particular, we ask whether it is the optimal measure for the transmission of information from a preparation to a measurement in some suitably defined scenario. We identify a scenario in which this is indeed the case, but our results suggest that an underlying real-Hilbert-space structure would be needed to realize the optimization in a natural way. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

12 pages, 1622 KiB

Open AccessArticle

Considerations on the Relativity of Quantum Irrealism

by Nicholas G. Engelbert and Renato M. Angelo

Entropy 2023, 25(4), 603; https://doi.org/10.3390/e25040603 - 1 Apr 2023

Cited by 2 | Viewed by 1226

Abstract

The study of quantum resources in the relativistic limit has attracted attention over the last couple of decades, mostly due to the observation that the spin-momentum entanglement is not Lorentz covariant. In this work, we take the investigations of relativistic quantum information a [...] Read more.

The study of quantum resources in the relativistic limit has attracted attention over the last couple of decades, mostly due to the observation that the spin-momentum entanglement is not Lorentz covariant. In this work, we take the investigations of relativistic quantum information a step further, bringing the foundational question of realism to the discussion. In particular, we examine whether Lorentz boosts can affect quantum irrealism—an instance related to the violations imposed by quantum mechanics onto a certain notion of realism. To this end, we adopt as a theoretical platform a model of a relativistic particle traveling through a Mach–Zehnder interferometer. We then compare the quantum irrealism assessed from two different inertial frames in relative motion. In consonance with recent findings in the context of quantum reference frames, our results suggest that the notion of physical realism is not absolute. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures

Figure 1

Other

Jump to: Research

11 pages, 308 KiB

Open AccessPerspective

Postulating the Unicity of the Macroscopic Physical World

by Mathias Van Den Bossche and Philippe Grangier

Entropy 2023, 25(12), 1600; https://doi.org/10.3390/e25121600 - 29 Nov 2023

Viewed by 839

Abstract

We argue that a clear view of quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows for a framework [...] Read more.

We argue that a clear view of quantum mechanics is obtained by considering that the unicity of the macroscopic world is a fundamental postulate of physics, rather than an issue that must be mathematically justified or demonstrated. This postulate allows for a framework in which quantum mechanics can be constructed in a complete mathematically consistent way. This is made possible by using general operator algebras to extend the mathematical description of the physical world toward macroscopic systems. Such an approach goes beyond the usual type-I operator algebras used in standard textbook quantum mechanics. This avoids a major pitfall, which is the temptation to make the usual type-I formalism ’universal’. This may also provide a meta-framework for both classical and quantum physics, shedding new light on ancient conceptual antagonisms and clarifying the status of quantum objects. Beyond exploring remote corners of quantum physics, we expect these ideas to be helpful to better understand and develop quantum technologies. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

► Show Figures