Research

15 pages, 1451 KiB

Open AccessArticle

Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise

by Arunava Majumder, Harshank Shrotriya and Leong-Chuan Kwek

Entropy 2021, 23(6), 685; https://0-doi-org.brum.beds.ac.uk/10.3390/e23060685 - 28 May 2021

Viewed by 2202

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise [...] Read more.

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ ‘quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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18 pages, 1488 KiB

Open AccessArticle

Performance Improvement of Discretely Modulated Continuous-Variable Quantum Key Distribution with Untrusted Source via Heralded Hybrid Linear Amplifier

by Kunlin Zhou, Xuelin Wu, Yun Mao, Zhiya Chen, Qin Liao and Ying Guo

Entropy 2020, 22(8), 882; https://0-doi-org.brum.beds.ac.uk/10.3390/e22080882 - 12 Aug 2020

Viewed by 2002

Abstract

In practical quantum communication networks, the scheme of continuous-variable quantum key distribution (CVQKD) faces a challenge that the entangled source is controlled by a malicious eavesdropper, and although it still can generate a positive key rate and security, its performance needs to be [...] Read more.

In practical quantum communication networks, the scheme of continuous-variable quantum key distribution (CVQKD) faces a challenge that the entangled source is controlled by a malicious eavesdropper, and although it still can generate a positive key rate and security, its performance needs to be improved, especially in secret key rate and maximum transmission distance. In this paper, we proposed a method based on the four-state discrete modulation and a heralded hybrid linear amplifier to enhance the performance of CVQKD where the entangled source originates from malicious eavesdropper. The four-state CVQKD encodes information by nonorthogonal coherent states in phase space. It has better transmission distance than Gaussian modulation counterpart, especially at low signal-to-noise ratio (SNR). Moreover, the hybrid linear amplifier concatenates a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), which can improve the probability of amplification success and reduce the noise penalty caused by the measurement. Furthermore, the hybrid linear amplifier can raise the SNR of CVQKD and tune between two types of performance for high-gain mode and high noise-reduction mode, therefore it can extend the maximal transmission distance while the entangled source is untrusted. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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35 pages, 791 KiB

Open AccessArticle

Wave–Particle–Entanglement–Ignorance Complementarity for General Bipartite Systems

by Wei Wu and Jin Wang

Entropy 2020, 22(8), 813; https://0-doi-org.brum.beds.ac.uk/10.3390/e22080813 - 24 Jul 2020

Cited by 4 | Viewed by 2064

Abstract

Wave–particle duality as the defining characteristic of quantum objects is a typical example of the principle of complementarity. The wave–particle–entanglement (WPE) complementarity, initially developed for two-qubit systems, is an extended form of complementarity that combines wave–particle duality with a previously missing ingredient, quantum [...] Read more.

Wave–particle duality as the defining characteristic of quantum objects is a typical example of the principle of complementarity. The wave–particle–entanglement (WPE) complementarity, initially developed for two-qubit systems, is an extended form of complementarity that combines wave–particle duality with a previously missing ingredient, quantum entanglement. For two-qubit systems in mixed states, the WPE complementarity was further completed by adding yet another piece that characterizes ignorance, forming the wave–particle–entanglement–ignorance (WPEI) complementarity. A general formulation of the WPEI complementarity can not only shed new light on fundamental problems in quantum mechanics, but can also have a wide range of experimental and practical applications in quantum-mechanical settings. The purpose of this study is to establish the WPEI complementarity for general multi-dimensional bipartite systems in pure or mixed states, and extend its range of applications to incorporate hierarchical and infinite-dimensional bipartite systems. The general formulation is facilitated by well-motivated generalizations of the relevant quantities. When faced with different directions of extensions to take, our guiding principle is that the formulated complementarity should be as simple and powerful as possible. We find that the generalized form of the WPEI complementarity contains unequal-weight averages reflecting the difference in the subsystem dimensions, and that the tangle, instead of the squared concurrence, serves as a more suitable entanglement measure in the general scenario. Two examples, a finite-dimensional bipartite system in mixed states and an infinite-dimensional bipartite system in pure states, are studied in detail to illustrate the general formalism. We also discuss our results in connection with some previous work. The WPEI complementarity for general finite-dimensional bipartite systems may be tested in multi-beam interference experiments, while the second example we studied may facilitate future experimental investigations on complementarity in infinite-dimensional bipartite systems. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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24 pages, 10627 KiB

Open AccessArticle

Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems

by Iulia Ghiu, Roberto Grimaudo, Tatiana Mihaescu, Aurelian Isar and Antonino Messina

Entropy 2020, 22(7), 785; https://0-doi-org.brum.beds.ac.uk/10.3390/e22070785 - 18 Jul 2020

Cited by 13 | Viewed by 2916

Abstract

We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical [...] Read more.

We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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12 pages, 623 KiB

Open AccessArticle

Nonclassical Effects Based on Husimi Distributions in Two Open Cavities Linked by an Optical Waveguide

by Abdel-Baset A. Mohamed and Hichem Eleuch

Entropy 2020, 22(7), 767; https://0-doi-org.brum.beds.ac.uk/10.3390/e22070767 - 13 Jul 2020

Cited by 3 | Viewed by 1714

Abstract

Nonclassical effects are investigated in a system formed by two quantum wells, each of which is inside an open cavity. The cavities are spatially separated, linked by a fiber, and filled with a linear optical medium. Based on Husimi distributions (HDs) and Wehrl [...] Read more.

Nonclassical effects are investigated in a system formed by two quantum wells, each of which is inside an open cavity. The cavities are spatially separated, linked by a fiber, and filled with a linear optical medium. Based on Husimi distributions (HDs) and Wehrl entropy, we explore the effects of the physical parameters on the generation and the robustness of the mixedness and HD information in the phase space. The generated quantum coherence and the HD information depend crucially on the cavity-exciton and fiber cavity couplings as well as on the optical medium density. The HD information and purity are lost due to the dissipation. This loss may be inhibited by increasing the optical susceptibility as well as the couplings of the exciton-cavity and the fiber-cavity. These parameters control the regularity, amplitudes, and frequencies of the generated mixedness. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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9 pages, 275 KiB

Open AccessArticle

In Praise of Quantum Uncertainty

by Eliahu Cohen and Avishy Carmi

Entropy 2020, 22(3), 302; https://0-doi-org.brum.beds.ac.uk/10.3390/e22030302 - 06 Mar 2020

Cited by 6 | Viewed by 2842

Abstract

Quantum uncertainty has a tremendous explanatory power. Coherent superposition, quantum equations of motion, entanglement, nonlocal correlations, dynamical nonlocality, contextuality, discord, counterfactual protocols, weak measurements, quantization itself, and even preservation of causality can be traced back to quantum uncertainty. We revisit and extend our [...] Read more.

Quantum uncertainty has a tremendous explanatory power. Coherent superposition, quantum equations of motion, entanglement, nonlocal correlations, dynamical nonlocality, contextuality, discord, counterfactual protocols, weak measurements, quantization itself, and even preservation of causality can be traced back to quantum uncertainty. We revisit and extend our previous works, as well as some other works of the community, in order to account for the above claims. Special emphasis is given to the connection between uncertainty and nonlocality, two notions which evolved quite independently and may seem distinct but, in fact, are tightly related. Indeterminism, or more precisely, locally consistent indeterminism, should be understood as the enabler of most quantum phenomena (and possibly all of them). Full article

(This article belongs to the Special Issue Quantum Entanglement)

9 pages, 244 KiB

Open AccessArticle

A Private Quantum Bit String Commitment

by Mariana Gama, Paulo Mateus and André Souto

Entropy 2020, 22(3), 272; https://0-doi-org.brum.beds.ac.uk/10.3390/e22030272 - 27 Feb 2020

Cited by 2 | Viewed by 2524

Abstract

We propose an entanglement-based quantum bit string commitment protocol whose composability is proven in the random oracle model. This protocol has the additional property of preserving the privacy of the committed message. Even though this property is not resilient against man-in-the-middle attacks, this [...] Read more.

We propose an entanglement-based quantum bit string commitment protocol whose composability is proven in the random oracle model. This protocol has the additional property of preserving the privacy of the committed message. Even though this property is not resilient against man-in-the-middle attacks, this threat can be circumvented by considering that the parties communicate through an authenticated channel. The protocol remains secure and private (but not composable) if we realize the random oracles as physical unclonable functions (PUFs) in the so-called bad PUF model. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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29 pages, 1577 KiB

Open AccessArticle

Theory of Quantum Path Entanglement and Interference with Multiplane Diffraction of Classical Light Sources

by Burhan Gulbahar

Entropy 2020, 22(2), 246; https://0-doi-org.brum.beds.ac.uk/10.3390/e22020246 - 21 Feb 2020

Cited by 2 | Viewed by 3204

Abstract

Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource [...] Read more.

Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger–Horne–Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman’s path integral approach. Leggett–Garg inequality as temporal analog of Bell’s inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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8 pages, 473 KiB

Open AccessArticle

Non-Monogamy of Spatio-Temporal Correlations and the Black Hole Information Loss Paradox

by Chiara Marletto, Vlatko Vedral, Salvatore Virzì, Enrico Rebufello, Alessio Avella, Fabrizio Piacentini, Marco Gramegna, Ivo Pietro Degiovanni and Marco Genovese

Entropy 2020, 22(2), 228; https://0-doi-org.brum.beds.ac.uk/10.3390/e22020228 - 18 Feb 2020

Cited by 5 | Viewed by 2469

Abstract

Pseudo-density matrices are a generalisation of quantum states and do not obey monogamy of quantum correlations. Could this be the solution to the paradox of information loss during the evaporation of a black hole? In this paper we discuss this possibility, providing a [...] Read more.

Pseudo-density matrices are a generalisation of quantum states and do not obey monogamy of quantum correlations. Could this be the solution to the paradox of information loss during the evaporation of a black hole? In this paper we discuss this possibility, providing a theoretical proposal to extend quantum theory with these pseudo-states to describe the statistics arising in black-hole evaporation. We also provide an experimental demonstration of this theoretical proposal, using a simulation in optical regime, that tomographically reproduces the correlations of the pseudo-density matrix describing this physical phenomenon. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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7 pages, 261 KiB

Open AccessArticle

A Note on the Hierarchy of Quantum Measurement Incompatibilities

by Bao-Zhi Sun, Zhi-Xi Wang, Xianqing Li-Jost and Shao-Ming Fei

Entropy 2020, 22(2), 161; https://0-doi-org.brum.beds.ac.uk/10.3390/e22020161 - 30 Jan 2020

Cited by 1 | Viewed by 1867

Abstract

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, [...] Read more.

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, we present a complete classification of the incompatibility of a given measurement assemblage with n members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program. Full article

(This article belongs to the Special Issue Quantum Entanglement)

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