Entropy

Editorial

Jump to: Research

4 pages, 175 KiB

Open AccessEditorial

Entropy in Foundations of Quantum Physics

by Marcin Pawłowski

Entropy 2020, 22(3), 371; https://doi.org/10.3390/e22030371 - 24 Mar 2020

Viewed by 3298

Abstract

Entropy can be used in studies on foundations of quantum physics in many different ways, each of them using different properties of this mathematical object [...] Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

Research

Jump to: Editorial

20 pages, 410 KiB

Open AccessArticle

Hypergraph Contextuality

by Mladen Pavičić

Entropy 2019, 21(11), 1107; https://doi.org/10.3390/e21111107 - 12 Nov 2019

Cited by 9 | Viewed by 2995

Abstract

Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum [...] Read more.

Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual sets, that is, sets of quantum observables capable of revealing quantum contextuality for any quantum state of a given dimension. There are two major classes of state-independent contextual sets—the Kochen-Specker ones and the operator-based ones. In this paper, we present a third, hypergraph-based class of contextual sets. Hypergraph inequalities serve as a measure of contextuality. We limit ourselves to qutrits and obtain thousands of 3-dim contextual sets. The simplest of them involves only 5 quantum observables, thus enabling a straightforward implementation. They also enable establishing new entropic contextualities. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Graphical abstract

37 pages, 397 KiB

Open AccessFeature PaperArticle

The Entropic Dynamics Approach to Quantum Mechanics

by Ariel Caticha

Entropy 2019, 21(10), 943; https://doi.org/10.3390/e21100943 - 26 Sep 2019

Cited by 18 | Viewed by 3486

Abstract

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified [...] Read more.

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures—which is a Hamilton-Killing flow in phase space—is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

12 pages, 317 KiB

Open AccessArticle

A New Mechanism of Open System Evolution and Its Entropy Using Unitary Transformations in Noncomposite Qudit Systems

by Julio A. López-Saldívar, Octavio Castaños, Margarita A. Man’ko and Vladimir I. Man’ko

Entropy 2019, 21(8), 736; https://doi.org/10.3390/e21080736 - 27 Jul 2019

Cited by 9 | Viewed by 2719

Abstract

The evolution of an open system is usually associated with the interaction of the system with an environment. A new method to study the open-type system evolution of a qubit (two-level atom) state is established. This evolution is determined by a unitary transformation [...] Read more.

The evolution of an open system is usually associated with the interaction of the system with an environment. A new method to study the open-type system evolution of a qubit (two-level atom) state is established. This evolution is determined by a unitary transformation applied to the qutrit (three-level atom) state, which defines the qubit subsystems. This procedure can be used to obtain different qubit quantum channels employing unitary transformations into the qutrit system. In particular, we study the phase damping and spontaneous-emission quantum channels. In addition, we mention a proposal for quasiunitary transforms of qubits, in view of the unitary transform of the total qutrit system. The experimental realization is also addressed. The probability representation of the evolution and its information-entropic characteristics are considered. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

15 pages, 364 KiB

Open AccessArticle

Uniqueness of Minimax Strategy in View of Minimum Error Discrimination of Two Quantum States

by Jihwan Kim, Donghoon Ha and Younghun Kwon

Entropy 2019, 21(7), 671; https://doi.org/10.3390/e21070671 - 9 Jul 2019

Cited by 4 | Viewed by 3385

Abstract

This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the [...] Read more.

This study considers the minimum error discrimination of two quantum states in terms of a two-party zero-sum game, whose optimal strategy is a minimax strategy. A minimax strategy is one in which a sender chooses a strategy for a receiver so that the receiver may obtain the minimum information about quantum states, but the receiver performs an optimal measurement to obtain guessing probability for the quantum ensemble prepared by the sender. Therefore, knowing whether the optimal strategy of the game is unique is essential. This is because there is no alternative if the optimal strategy is unique. This paper proposes the necessary and sufficient condition for an optimal strategy of the sender to be unique. Also, we investigate the quantum states that exhibit the minimum guessing probability when a sender’s minimax strategy is unique. Furthermore, we show that a sender’s minimax strategy and a receiver’s minimum error strategy cannot be unique if one can simultaneously diagonalize two quantum states, with the optimal measurement of the minimax strategy. This implies that a sender can confirm that the optimal strategy of only a single side (a sender or a receiver but not both of them) is unique by preparing specific quantum states. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

15 pages, 1061 KiB

Open AccessArticle

Improving Parameter Estimation of Entropic Uncertainty Relation in Continuous-Variable Quantum Key Distribution

by Ziyang Chen, Yichen Zhang, Xiangyu Wang, Song Yu and Hong Guo

Entropy 2019, 21(7), 652; https://doi.org/10.3390/e21070652 - 2 Jul 2019

Cited by 24 | Viewed by 3335

Abstract

The entropic uncertainty relation (EUR) is of significant importance in the security proof of continuous-variable quantum key distribution under coherent attacks. The parameter estimation in the EUR method contains the estimation of the covariance matrix (CM), as well as the max-entropy. The discussions [...] Read more.

The entropic uncertainty relation (EUR) is of significant importance in the security proof of continuous-variable quantum key distribution under coherent attacks. The parameter estimation in the EUR method contains the estimation of the covariance matrix (CM), as well as the max-entropy. The discussions in previous works have not involved the effect of finite-size on estimating the CM, which will further affect the estimation of leakage information. In this work, we address this issue by adapting the parameter estimation technique to the EUR analysis method under composable security frameworks. We also use the double-data modulation method to improve the parameter estimation step, where all the states can be exploited for both parameter estimation and key generation; thus, the statistical fluctuation of estimating the max-entropy disappears. The result shows that the adapted method can effectively estimate parameters in EUR analysis. Moreover, the double-data modulation method can, to a large extent, save the key consumption, which further improves the performance in practical implementations of the EUR. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

13 pages, 305 KiB

Open AccessArticle

On the Exact Variance of Tsallis Entanglement Entropy in a Random Pure State

by Lu Wei

Entropy 2019, 21(5), 539; https://doi.org/10.3390/e21050539 - 27 May 2019

Cited by 16 | Viewed by 3408

Abstract

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an [...] Read more.

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

11 pages, 1030 KiB

Open AccessArticle

Probabilistic Resumable Quantum Teleportation of a Two-Qubit Entangled State

by Zhan-Yun Wang, Yi-Tao Gou, Jin-Xing Hou, Li-Ke Cao and Xiao-Hui Wang

Entropy 2019, 21(4), 352; https://doi.org/10.3390/e21040352 - 1 Apr 2019

Cited by 7 | Viewed by 3733

Abstract

We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially [...] Read more.

We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

12 pages, 1274 KiB

Open AccessArticle

Quantum Discord, Thermal Discord, and Entropy Generation in the Minimum Error Discrimination Strategy

by Omar Jiménez, Miguel Angel Solís-Prosser, Leonardo Neves and Aldo Delgado

Entropy 2019, 21(3), 263; https://doi.org/10.3390/e21030263 - 8 Mar 2019

Cited by 6 | Viewed by 5117

Abstract

We study the classical and quantum correlations in the minimum error discrimination (ME) of two non-orthogonal pure quantum states. In particular, we consider quantum discord, thermal discord and entropy generation. We show that ME allows one to reach the accessible information between the [...] Read more.

We study the classical and quantum correlations in the minimum error discrimination (ME) of two non-orthogonal pure quantum states. In particular, we consider quantum discord, thermal discord and entropy generation. We show that ME allows one to reach the accessible information between the two involved parties, Alice and Bob, in the discrimination process. We determine the amount of quantum discord that is consumed in the ME and show that the entropy generation is, in general, higher than the thermal discord. However, in certain cases the entropy generation is very close to thermal discord, which indicates that, in these cases, the process generates the least possible entropy. Moreover, we also study the ME process as a thermodynamic cycle and we show that it is in agreement with the second law of thermodynamics. Finally, we study the relation between the accessible information and the optimum success probability in ME. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

28 pages, 867 KiB

Open AccessArticle

Representation Lost: The Case for a Relational Interpretation of Quantum Mechanics

by Raffael Krismer

Entropy 2018, 20(12), 975; https://doi.org/10.3390/e20120975 - 15 Dec 2018

Cited by 7 | Viewed by 3968

Abstract

Contemporary non-representationalist interpretations of the quantum state (especially QBism, neo-Copenhagen views, and the relational interpretation) maintain that quantum states codify observer-relative information. This paper provides an extensive defense of such views, while emphasizing the advantages of, specifically, the relational interpretation. [...] Read more.

Contemporary non-representationalist interpretations of the quantum state (especially QBism, neo-Copenhagen views, and the relational interpretation) maintain that quantum states codify observer-relative information. This paper provides an extensive defense of such views, while emphasizing the advantages of, specifically, the relational interpretation. The argument proceeds in three steps: (1) I present a classical example (which exemplifies the spirit of the relational interpretation) to illustrate why some of the most persistent charges against non-representationalism have been misguided. (2) The special focus is placed on dynamical evolution. Non-representationalists often motivate their views by interpreting the collapse postulate as the quantum mechanical analogue of Bayesian probability updating. However, it is not clear whether one can also interpret the Schrödinger equation as a form of rational opinion updating. Using results due to Hughes & van Fraassen as well as Lisi, I argue that unitary evolution has a counterpart in classical probability theory: in both cases (quantum and classical) probabilities relative to a non-participating observer evolve according to an entropy maximizing principle (and can be interpreted as rational opinion updating). (3) Relying on a thought-experiment by Frauchiger and Renner, I discuss the differences between quantum and classical probability models. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

15 pages, 952 KiB

Open AccessArticle

Some Consequences of the Thermodynamic Cost of System Identification

by Chris Fields

Entropy 2018, 20(10), 797; https://doi.org/10.3390/e20100797 - 17 Oct 2018

Cited by 15 | Viewed by 3757

Abstract

The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made. [...] Read more.

The concept of a “system” is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which “pointer state” measurements are to be made. It is shown that system identification is at best approximate, even in a finite world, and that violations of the Leggett–Garg and Bell/CHSH (Clauser-Horne-Shimony-Holt) inequalities emerge naturally as requirements for successful system identification. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

15 pages, 2738 KiB

Open AccessArticle

Image Thresholding Segmentation on Quantum State Space

by Xiangluo Wang, Chunlei Yang, Guo-Sen Xie and Zhonghua Liu

Entropy 2018, 20(10), 728; https://doi.org/10.3390/e20100728 - 23 Sep 2018

Cited by 10 | Viewed by 4609

Abstract

Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, [...] Read more.

Aiming to implement image segmentation precisely and efficiently, we exploit new ways to encode images and achieve the optimal thresholding on quantum state space. Firstly, the state vector and density matrix are adopted for the representation of pixel intensities and their probability distribution, respectively. Then, the method based on global quantum entropy maximization (GQEM) is proposed, which has an equivalent object function to Otsu’s, but gives a more explicit physical interpretation of image thresholding in the language of quantum mechanics. To reduce the time consumption for searching for optimal thresholds, the method of quantum lossy-encoding-based entropy maximization (QLEEM) is presented, in which the eigenvalues of density matrices can give direct clues for thresholding, and then, the process of optimal searching can be avoided. Meanwhile, the QLEEM algorithm achieves two additional effects: (1) the upper bound of the thresholding level can be implicitly determined according to the eigenvalues; and (2) the proposed approaches ensure that the local information in images is retained as much as possible, and simultaneously, the inter-class separability is maximized in the segmented images. Both of them contribute to the structural characteristics of images, which the human visual system is highly adapted to extract. Experimental results show that the proposed methods are able to achieve a competitive quality of thresholding and the fastest computation speed compared with the state-of-the-art methods. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

14 pages, 523 KiB

Open AccessArticle

Quantum Quantifiers for an Atom System Interacting with a Quantum Field Based on Pseudoharmonic Oscillator States

by Bahaaudin Mohammadnoor Raffah and Kamal Berrada

Entropy 2018, 20(8), 607; https://doi.org/10.3390/e20080607 - 16 Aug 2018

Cited by 4 | Viewed by 3436

Abstract

We develop a useful model considering an atom-field system interaction in the framework of pseudoharmonic oscillators. We examine qualitatively the different physical quantities for a two-level atom (TLA) system interacting with a quantized coherent field in the context of photon-added coherent states of [...] Read more.

We develop a useful model considering an atom-field system interaction in the framework of pseudoharmonic oscillators. We examine qualitatively the different physical quantities for a two-level atom (TLA) system interacting with a quantized coherent field in the context of photon-added coherent states of pseudoharmonic oscillators. Using these coherent states, we solve the model that exhibits the interaction between the TLA and field associated with these kinds of potentials. We analyze the temporal evolution of the entanglement, statistical properties, geometric phase and squeezing entropies. Finally, we show the relationship between the physical quantities and their dynamics in terms of the physical parameters. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

12 pages, 1194 KiB

Open AccessArticle

Enhancing of Self-Referenced Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction

by Hai Zhong, Yijun Wang, Xudong Wang, Qin Liao, Xiaodong Wu and Ying Guo

Entropy 2018, 20(8), 578; https://doi.org/10.3390/e20080578 - 6 Aug 2018

Cited by 10 | Viewed by 3321

Abstract

The scheme of the self-referenced continuous-variable quantum key distribution (SR CV-QKD) has been experimentally demonstrated. However, because of the finite dynamics of Alice’s amplitude modulator, there will be an extra excess noise that is proportional to the amplitude of the reference pulse, while [...] Read more.

The scheme of the self-referenced continuous-variable quantum key distribution (SR CV-QKD) has been experimentally demonstrated. However, because of the finite dynamics of Alice’s amplitude modulator, there will be an extra excess noise that is proportional to the amplitude of the reference pulse, while the maximal transmission distance of this scheme is positively correlated with the amplitude of the reference pulse. Therefore, there is a trade-off between the maximal transmission distance and the amplitude of the reference pulse. In this paper, we propose the scheme of SR CV-QKD with virtual photon subtraction, which not only has no need for the use of a high intensity reference pulse to improve the maximal transmission distance, but also has no demand of adding complex physical operations to the original self-referenced scheme. Compared to the original scheme, our simulation results show that a considerable extension of the maximal transmission distance can be obtained when using a weak reference pulse, especially for one-photon subtraction. We also find that our scheme is sensible with the detector’s electronic noise at reception. A longer maximal transmission distance can be achieved for lower electronic noise. Moreover, our scheme has a better toleration of excess noise compared to the original self-referenced scheme, which implies the advantage of using virtual photon subtraction to increase the maximal tolerable excess noise for distant users. These results suggest that our scheme can make the SR CV-QKD from the laboratory possible for practical metropolitan area application. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

13 pages, 6268 KiB

Open AccessArticle

Security Analysis of Unidimensional Continuous-Variable Quantum Key Distribution Using Uncertainty Relations

by Pu Wang, Xuyang Wang and Yongmin Li

Entropy 2018, 20(3), 157; https://doi.org/10.3390/e20030157 - 1 Mar 2018

Cited by 10 | Viewed by 3817

Abstract

We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using [...] Read more.

We study the equivalence between the entanglement-based scheme and prepare-and-measure scheme of unidimensional (UD) continuous-variable quantum key distribution protocol. Based on this equivalence, the physicality and security of the UD coherent-state protocols in the ideal detection and realistic detection conditions are investigated using the Heisenberg uncertainty relation, respectively. We also present a method to increase both the secret key rates and maximal transmission distances of the UD coherent-state protocol by adding an optimal noise to the reconciliation side. It is expected that our analysis will aid in the practical applications of the UD protocol. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

12 pages, 389 KiB

Open AccessArticle

Tsirelson’s Bound Prohibits Communication through a Disconnected Channel

by Avishy Carmi and Daniel Moskovich

Entropy 2018, 20(3), 151; https://doi.org/10.3390/e20030151 - 27 Feb 2018

Cited by 5 | Viewed by 3628

Abstract

Why does nature only allow nonlocal correlations up to Tsirelson’s bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson’s bound is violated. This provides [...] Read more.

Why does nature only allow nonlocal correlations up to Tsirelson’s bound and not beyond? We construct a channel whose input is statistically independent of its output, but through which communication is nevertheless possible if and only if Tsirelson’s bound is violated. This provides a statistical justification for Tsirelson’s bound on nonlocal correlations in a bipartite setting. Full article

(This article belongs to the Special Issue Entropy in Foundations of Quantum Physics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Entropy in Foundations of Quantum Physics

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (16 papers)

Editorial

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI