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Entropy, Quantum Information and Entanglement

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 August 2024) | Viewed by 6785

Special Issue Editor


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Guest Editor
Information Directorate, Air Force Research Laboratory, Rome, NY 13441, USA
Interests: quantum computation; quantum information processing; quantum entanglement; quantum algorithms; quantum error correction; numerical simulations of quantum computers; decoherence; HPC; relativistic quantum information; geometry and topology of quantum states/information

Special Issue Information

Dear Colleagues,

Classical information theory is primarily concerned with the problem of sending classical information over communications channels which operate in accordance with the laws of classical physics. Quantum information theory is similarly motivated by the study of communication channels but encompassing a much wider domain of applications based on quantum mechanics. The three fundamental goals of quantum information theory are concerned with (i) identifying new classes of static resources, which we identify as types of ‘information’; (ii) new elementary classes of dynamical processes, which we identify as types of ‘information processing’; and, lastly (iii), means and measures to quantify the resource tradeoffs incurred when performing elementary quantum dynamical processes.

One of the entirely new classes of static resources allowed for by quantum mechanics is quantum entanglement, whereby an entangled state provides us with more information about the total system than about its subsystems. The applications of entanglement are now well known to manifold, from applied applications such as cryptography, metrology, and communication/networking computing to new fundamental insights into particle and black hole physics, involving the entanglement of the vacuum and across horizons.

Essential to the study of entanglement is a fundamental understating of distinguishability, which is the measure of uncertainty in a given probability distribution inherent or generated in quantum states. Quantum distinguishability never decreases, and correlations cannot increase without subsystem interactions. Here, the concept of entropy, and measures of entropy, play a central role. In an entangled state, the entropy of a subsystem can be greater than the entropy of the total system only when the state is entangled. In other words, the subsystems of an entangled system may exhibit more disorder than the system as a whole, a phenomena that in the classical world never occurs.

The aim of this Special Issue is to collect works exhibiting novel connections amongst the topics of entropy, quantum information, and entanglement. Special attention to the role played by entropic arguments in such connections will be warmly welcome.

Dr. Paul M. Alsing
Guest Editor

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Keywords

  • entropy
  • entanglement
  • quantum information
  • measures of indistinguishability/fidelity of quantum states
  • thermodynamics
  • black hole information paradox
  • vacuum entanglement and particle physics

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Published Papers (4 papers)

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Research

22 pages, 8302 KiB  
Article
Refraction of the Two-Photon Multimode Field via a Three-Level Atom
by Trever Harborth and Yuri Rostovtsev
Entropy 2025, 27(1), 71; https://doi.org/10.3390/e27010071 - 15 Jan 2025
Viewed by 1031
Abstract
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level [...] Read more.
Classically, the refractive index of a medium is due to a response on said medium from an electromagnetic field. It has been shown that a single two-level atom interacting with a single photon undergoes dispersion. The following extends that analyses to a three-level system interacting with two photons. Analysis of the system is completed both numerically for all photonic field modes, and analytically for an adiabatic solution of a single field mode. The findings are not only interesting for understanding additional physical phenomena due to the increased complexity of a three-level, two-photon system, but are also necessary for advancing applications such as quantum communications, quantum computation, and quantum information. Full article
(This article belongs to the Special Issue Entropy, Quantum Information and Entanglement)
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16 pages, 311 KiB  
Article
Communication Complexity of Entanglement-Assisted Multi-Party Computation
by Ruoyu Meng and Aditya Ramamoorthy
Entropy 2024, 26(11), 896; https://doi.org/10.3390/e26110896 - 23 Oct 2024
Viewed by 743
Abstract
We consider a quantum and a classical version of a multi-party function computation problem with n players, where players 2,,n need to communicate appropriate information to player 1 so that a “generalized” inner product function with an appropriate promise [...] Read more.
We consider a quantum and a classical version of a multi-party function computation problem with n players, where players 2,,n need to communicate appropriate information to player 1 so that a “generalized” inner product function with an appropriate promise can be calculated. In the quantum version of the protocol, the players have access to entangled qudits but the communication is still classical. The communication complexity of a given protocol is the total number of classical bits that need to be communicated. When n is prime, and for our chosen function, we exhibit a quantum protocol (with complexity (n1)(logn) bits) and a classical protocol (with complexity ((n1)2(logn2) bits)). Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols. Full article
(This article belongs to the Special Issue Entropy, Quantum Information and Entanglement)
14 pages, 1090 KiB  
Article
New Quantum Private Comparison Using Four-Particle Cluster State
by Min Hou, Yue Wu and Shibin Zhang
Entropy 2024, 26(6), 512; https://doi.org/10.3390/e26060512 - 14 Jun 2024
Cited by 7 | Viewed by 1083
Abstract
Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two [...] Read more.
Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two users, which constrained their scalability. In this paper, we propose a QPC protocol that leverages the entanglement correlation between particles in a four-particle cluster state. This protocol can compare the information of two groups of users within one protocol execution, with each group consisting of two users. A semi-honest third party (TP), who will not deviate from the protocol execution or conspire with any participant, is involved in assisting users to achieve private comparisons. Users encode their inputs into specific angles of rotational operations performed on the received quantum sequence, which is then sent back to TP. Security analysis shows that both external attacks and insider threats are ineffective at stealing private data. Finally, we compare our protocol with some previously proposed QPC protocols. Full article
(This article belongs to the Special Issue Entropy, Quantum Information and Entanglement)
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14 pages, 914 KiB  
Article
Pointer States and Quantum Darwinism with Two-Body Interactions
by Paul Duruisseau, Akram Touil and Sebastian Deffner
Entropy 2023, 25(12), 1573; https://doi.org/10.3390/e25121573 - 22 Nov 2023
Cited by 5 | Viewed by 3042
Abstract
Quantum Darwinism explains the emergence of classical objectivity within a quantum universe. However, to date, most research on quantum Darwinism has focused on specific models and their stationary properties. To further our understanding of the quantum-to-classical transition, it appears desirable to identify the [...] Read more.
Quantum Darwinism explains the emergence of classical objectivity within a quantum universe. However, to date, most research on quantum Darwinism has focused on specific models and their stationary properties. To further our understanding of the quantum-to-classical transition, it appears desirable to identify the general criteria a Hamiltonian has to fulfill to support classical reality. To this end, we categorize all N-qubit models with two-body interactions, and show that only those with separable interaction of the system and environment can support a pointer basis. We further demonstrate that “perfect” quantum Darwinism can only emerge if there are no intra-environmental interactions. Our analysis is complemented by solving the ensuing dynamics. We find that in systems exhibiting information scrambling, the dynamical emergence of classical objectivity directly competes with the non-local spread of quantum correlations. Our rigorous findings are illustrated through the numerical analysis of four representative models. Full article
(This article belongs to the Special Issue Entropy, Quantum Information and Entanglement)
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