Research

265 KiB

Open AccessArticle

by Valentina Baccetti, Viqar Husain and Daniel R. Terno

Entropy 2017, 19(1), 17; https://0-doi-org.brum.beds.ac.uk/10.3390/e19010017 - 30 Dec 2016

Cited by 11 | Viewed by 5050

The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element—forming of the event horizon before the evaporation begins—is not necessarily true, [...] Read more.

The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element—forming of the event horizon before the evaporation begins—is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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2043 KiB

Open AccessFeature PaperArticle

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

by Eduardo Jonathan Torres-Herrera, Jonathan Karp, Marco Távora and Lea F. Santos

Entropy 2016, 18(10), 359; https://0-doi-org.brum.beds.ac.uk/10.3390/e18100359 - 08 Oct 2016

Cited by 38 | Viewed by 6196

Abstract

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von [...] Read more.

We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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903 KiB

Open AccessArticle

Enhanced Energy Distribution for Quantum Information Heat Engines

by Jose M. Diaz de la Cruz and Miguel Angel Martin-Delgado

Entropy 2016, 18(9), 335; https://0-doi-org.brum.beds.ac.uk/10.3390/e18090335 - 14 Sep 2016

Cited by 8 | Viewed by 4816

Abstract

A new scenario for energy distribution, security and shareability is presented that assumes the availability of quantum information heat engines and a thermal bath. It is based on the convertibility between entropy and work in the presence of a thermal reservoir. Our approach [...] Read more.

A new scenario for energy distribution, security and shareability is presented that assumes the availability of quantum information heat engines and a thermal bath. It is based on the convertibility between entropy and work in the presence of a thermal reservoir. Our approach to the informational content of physical systems that are distributed between users is complementary to the conventional perspective of quantum communication. The latter places the value on the unpredictable content of the transmitted quantum states, while our interest focuses on their certainty. Some well-known results in quantum communication are reused in this context. Particularly, we describe a way to securely distribute quantum states to be used for unlocking energy from thermal sources. We also consider some multi-partite entangled and classically correlated states for a collaborative multi-user sharing of work extraction possibilities. In addition, the relation between the communication and work extraction capabilities is analyzed and written as an equation. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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1325 KiB

Open AccessArticle

Generalized Robustness of Contextuality

by Huixian Meng, Huaixin Cao, Wenhua Wang, Yajing Fan and Liang Chen

Entropy 2016, 18(9), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/e18090297 - 01 Sep 2016

Cited by 6 | Viewed by 4125

Abstract

Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC)

R_{C} (e)

of an empirical model e against non-contextual noises was introduced and discussed in Science [...] Read more.

Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC)

R_{C} (e)

of an empirical model e against non-contextual noises was introduced and discussed in Science China Physics, Mechanics and Astronomy (59(4) and 59(9), 2016). Because noises are not always non-contextual, this paper introduces and discusses the generalized robustness of contextuality (GRoC)

R_{g} (e)

of an empirical model e against general noises. It is proven that

R_{g} (e) = 0

if and only if e is non-contextual. This means that the quantity

R_{g}

can be used to distinguish contextual empirical models from non-contextual ones. It is also shown that the function

R_{g}

is convex on the set of all empirical models and continuous on the set of all no-signaling empirical models. For any two empirical models e and f such that the generalized relative robustness of e with respect to f is finite, a fascinating relationship between the GRoCs of e and f is proven, which reads

R_{g} (e) R_{g} (f) \leq 1

. Lastly, for any n-cycle contextual box e, a relationship between the GRoC

R_{g} (e)

and the extent

Δ_{e}

of violating the non-contextual inequalities is established. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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583 KiB

Open AccessArticle

Novel Criteria for Deterministic Remote State Preparation via the Entangled Six-Qubit State

by Gang Xu, Xiu-Bo Chen, Zhao Dou, Jing Li, Xin Liu and Zongpeng Li

Entropy 2016, 18(7), 267; https://0-doi-org.brum.beds.ac.uk/10.3390/e18070267 - 20 Jul 2016

Cited by 20 | Viewed by 4317

Abstract

In this paper, our concern is to design some criteria for deterministic remote state preparation for preparing an arbitrary three-particle state via a genuinely entangled six-qubit state. First, we put forward two schemes in both the real and complex Hilbert space, respectively. Using [...] Read more.

In this paper, our concern is to design some criteria for deterministic remote state preparation for preparing an arbitrary three-particle state via a genuinely entangled six-qubit state. First, we put forward two schemes in both the real and complex Hilbert space, respectively. Using an appropriate set of eight-qubit measurement basis, the remote three-qubit preparation is completed with unit success probability. Departing from previous research, our protocol has a salient feature in that the serviceable measurement basis only contains the initial coefficients and their conjugate values. By utilizing the permutation group, it is convenient to provide the permutation relationship between coefficients. Second, our ideas and methods can also be generalized to the situation of preparing an arbitrary N-particle state in complex case by taking advantage of Bell states as quantum resources. More importantly, criteria satisfied conditions for preparation with 100% success probability in complex Hilbert space is summarized. Third, the classical communication costs of our scheme are calculated to determine the classical recourses required. It is also worth mentioning that our protocol has higher efficiency and lower resource costs compared with the other papers. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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294 KiB

Open AccessArticle

On Two-Distillable Werner States

by Dragomir Ž. Đoković

Entropy 2016, 18(6), 216; https://0-doi-org.brum.beds.ac.uk/10.3390/e18060216 - 02 Jun 2016

Cited by 9 | Viewed by 3642

Abstract

We consider bipartite mixed states ρ in a

d \otimes d

quantum system. We say that ρ is PPT if its partial transpose

1 \otimes T (ρ)

is positive semidefinite, and otherwise ρ is NPT. The well-known Werner states are divided [...] Read more.

We consider bipartite mixed states ρ in a

d \otimes d

quantum system. We say that ρ is PPT if its partial transpose

1 \otimes T (ρ)

is positive semidefinite, and otherwise ρ is NPT. The well-known Werner states are divided into three types: (a) the separable states (the same as the PPT states); (b) the one-distillable states (necessarily NPT); and (c) the NPT states which are not one-distillable. We give several different formulations and provide further evidence for the validity of the conjecture that Werner states of type (c) are not two-distillable. Full article

(This article belongs to the Special Issue Quantum Information 2016)

1093 KiB

Open AccessArticle

Multiphoton Controllable Transport between Remote Resonators

by Wei Qin and Guilu Long

Entropy 2016, 18(6), 179; https://0-doi-org.brum.beds.ac.uk/10.3390/e18060179 - 27 May 2016

Cited by 1 | Viewed by 3467

Abstract

We develop a novel method for multiphoton controllable transport between remote resonators. Specifically, an auxiliary resonator is used to control the coherent long-range coupling of two spatially separated resonators, mediated by a coupled-resonator chain of arbitrary length. In this manner, an arbitrary multiphoton [...] Read more.

We develop a novel method for multiphoton controllable transport between remote resonators. Specifically, an auxiliary resonator is used to control the coherent long-range coupling of two spatially separated resonators, mediated by a coupled-resonator chain of arbitrary length. In this manner, an arbitrary multiphoton quantum state can be either transmitted through or reflected off the intermediate chain on demand, with very high fidelity. We find, on using a time-independent perturbative treatment, that quantum information leakage of an arbitrary Fock state is limited by two upper bounds, one for the transmitted case and the other for the reflected case. In principle, the two upper bounds can be made arbitrarily small, which is confirmed by numerical simulations. Full article

(This article belongs to the Special Issue Quantum Information 2016)

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337 KiB

Open AccessArticle

Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances

by Cécile Monthus

Entropy 2016, 18(4), 122; https://0-doi-org.brum.beds.ac.uk/10.3390/e18040122 - 01 Apr 2016

Cited by 25 | Viewed by 4755

Abstract

The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In [...] Read more.

The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent

0 < α < 1

anywhere between the area law

α = 0

and the volume law

α = 1

, as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value

ν = 1

for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality

ν \geq 2 / d

, so that there is no theoretical inconsistency with the best numerical measure

ν = 0.8 (3)

obtained by Luitz et al. (2015). Full article

(This article belongs to the Special Issue Quantum Information 2016)

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