Quantum Entanglement and Quantum Optics: Latest Advances and Prospects

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 7261

Special Issue Editor


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Guest Editor
Faculty of Physics, Yazd University, Yazd, Iran
Interests: quantum mechanics; quantum optics; classical mechanics; mathematical physics

Special Issue Information

Dear Colleagues,

Nowadays, entanglement phenomenon (of photons, phonons, atoms, superconducting qubits, magnons, and etc.) plays a key role in quantum optics researches and quantum information science and technologies. Motivated from this realization, we would like to invite original submissions to the Special Issue, "Quantum Entanglement and Quantum Optics: Latest Advances and Prospects". The subject of submissions is extended to the dynamical systems, in which the entangled states are produced, analyzed, quantified or even are used in setups to perform quantum teleportation protocols, quantum repeaters, entanglement swapping, and etc., either theoretically or experimentally. Moreover, we have particular attention to symmetric (for instance symmetric N-qubit systems) and ani-symmetric Hamiltonians in various interactions models containing atom-field interactions, the dynamics of which is of great importance in quantum information theory. In this regard, the construction of (genuinely) entangled (multipartite) quantum states based on the group theory, as well as in PT- and anti-PT-symmetric Hamiltonians, are particularly welcome. By this, we intend to gather, with your helps, a useful and enriched collection of the recent researches on entanglement that opens further research windows to the interested researchers in the field. Please find the keywords in below.

Prof. Dr. Mohammad Kazem Tavassoly
Guest Editor

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Keywords

  • entanglement in quantum information processing
  • theoretical production of entangled states
  • experimental generation of entangled states
  • entanglement in symmetric and anti-symmetric hamiltonians
  • entanglement detection
  • entanglement measures
  • applications of entanglement
  • quantum repeaters
  • quantum teleportation
  • entanglement swapping

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Published Papers (6 papers)

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Research

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20 pages, 361 KiB  
Article
The Separability Problem in Two Qubits Revisited
by Honorine Gnonfin and Laure Gouba
Symmetry 2023, 15(11), 2089; https://doi.org/10.3390/sym15112089 - 20 Nov 2023
Cited by 2 | Viewed by 1094
Abstract
In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in a two quantum bits (qubits) system, from the separability criterion based on Bell’s inequalities in 1964 to the recent separability criteria. Full article
21 pages, 1880 KiB  
Article
Entanglement and Symmetry Structure of N(= 3) Quantum Oscillators with Disparate Coupling Strengths in a Common Quantum Field Bath
by Jen-Tsung Hsiang and Bei-Lok Hu
Symmetry 2023, 15(11), 2064; https://doi.org/10.3390/sym15112064 - 14 Nov 2023
Viewed by 1030
Abstract
In this paper, we study the entanglement structure of a system of N quantum oscillators with distinctive coupling strengths, all linearly coupled to a common massless scalar quantum field. This study is helpful in characterizing the notion of an entanglement domain and its [...] Read more.
In this paper, we study the entanglement structure of a system of N quantum oscillators with distinctive coupling strengths, all linearly coupled to a common massless scalar quantum field. This study is helpful in characterizing the notion of an entanglement domain and its symmetry features, which is useful for understanding the interplay between different levels of structure in many-body quantum systems. The effect of the quantum field on the system is derived via the influence functional and the correlation functions are obtained from the solutions of the evolutionary operator of the reduced density matrix. They are then used to construct the covariance matrix, which forms the basis for our analysis of the structure of quantum entanglement in this open system. To make the physical features explicit, we consider a system of three quantum coupled oscillators placed at the vertices of an equilateral triangle with disparate pairwise couplings. We analyze the entanglement between one oscillator and the other two with equal (symmetric) and unequal (asymmetric) coupling strengths. As a physical illustration, we apply the results for these two different configurations to address some basic issues in macroscopic quantum phenomena from the quantum entanglement perspective. Full article
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0 pages, 629 KiB  
Article
RETRACTED: Envariance as a Symmetry in Quantum Mechanics and Applications to Statistical Mechanics
by Paul Bracken
Symmetry 2023, 15(10), 1923; https://doi.org/10.3390/sym15101923 - 16 Oct 2023
Cited by 1 | Viewed by 1126 | Retraction
Abstract
A quantum symmetry called entanglement-assisted invariance, also called envariance, is introduced. It is studied with respect to the process of performing quantum measurements. An apparatus which interacts with other physical systems, which are called environments, exchanges a single state with physical states equal [...] Read more.
A quantum symmetry called entanglement-assisted invariance, also called envariance, is introduced. It is studied with respect to the process of performing quantum measurements. An apparatus which interacts with other physical systems, which are called environments, exchanges a single state with physical states equal in number to that of the possible outcomes of the experiment. Correlations between the apparatus and environment give rise to a type of selection rule which prohibits the apparatus from appearing in a superposition corresponding to different eigenvalues of the pointer basis of the apparatus. The eigenspaces of this observable form a natural basis for the apparatus and determine the observable of the measured quantum system. It is also discussed how statistical mechanics can be formulated in terms of this symmetry. Full article
12 pages, 1574 KiB  
Article
Generation of Stable Entanglement in an Optomechanical System with Dissipative Environment: Linear-and-Quadratic Couplings
by Mehran Rafeie and Mohammad Kazem Tavassoly
Symmetry 2023, 15(9), 1770; https://doi.org/10.3390/sym15091770 - 15 Sep 2023
Cited by 2 | Viewed by 957
Abstract
In this paper, we present a theoretical scheme for the generation and manipulation of bipartite atom–atom entanglement in a dissipative optomechanical system containing two atoms in the presence of linear and nonlinear (quadratic) couplings. To achieve the goal of paper, we first obtain [...] Read more.
In this paper, we present a theoretical scheme for the generation and manipulation of bipartite atom–atom entanglement in a dissipative optomechanical system containing two atoms in the presence of linear and nonlinear (quadratic) couplings. To achieve the goal of paper, we first obtain the interaction Hamiltonian in the interaction picture, and then, by considering some resonance conditions and applying the rotating wave approximation, the effective Hamiltonian, which is independent of time, is derived. In the continuation, the system solution was obtained via solving the Lindblad master equation, which includes atomic, optical and mechanical dissipation effects. Finally, bipartite atom–atom entanglement is quantitatively discussed, by evaluating the negativity, which is a well-known measure of entanglement. Our numerical simulations show that a significant degree of entanglement can be reached via adjusting the system parameters. It is noticeable that the optical and mechanical decay rates play an important role in the quasi-stability and even stability of the obtained atom–atom entanglement. Full article
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Review

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30 pages, 666 KiB  
Review
From Entanglement to Universality: A Multiparticle Spacetime Algebra Approach to Quantum Computational Gates Revisited
by Carlo Cafaro, Newshaw Bahreyni and Leonardo Rossetti
Symmetry 2024, 16(6), 734; https://doi.org/10.3390/sym16060734 - 12 Jun 2024
Viewed by 960
Abstract
Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [...] Read more.
Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our application of geometric (Clifford) algebras (GAs) in quantum computing as originally presented in [C. Cafaro and S. Mancini, Adv. Appl. Clifford Algebras 21, 493 (2011)]. Our focus is on testing the usefulness of geometric algebras (GAs) techniques in two quantum computing applications. First, making use of the geometric algebra of a relativistic configuration space (namely multiparticle spacetime algebra or MSTA), we offer an explicit algebraic characterization of one- and two-qubit quantum states together with a MSTA description of one- and two-qubit quantum computational gates. In this first application, we devote special attention to the concept of entanglement, focusing on entangled quantum states and two-qubit entangling quantum gates. Second, exploiting the previously mentioned MSTA characterization together with the GA depiction of the Lie algebras SO3;R and SU2;C depending on the rotor group Spin+3,0 formalism, we focus our attention to the concept of universality in quantum computing by reevaluating Boykin’s proof on the identification of a suitable set of universal quantum gates. At the end of our mathematical exploration, we arrive at two main conclusions. Firstly, the MSTA perspective leads to a powerful conceptual unification between quantum states and quantum operators. More specifically, the complex qubit space and the complex space of unitary operators acting on them merge in a single multivectorial real space. Secondly, the GA viewpoint on rotations based on the rotor group Spin+3,0 carries both conceptual and computational advantages compared to conventional vectorial and matricial methods. Full article
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52 pages, 769 KiB  
Review
Quantum-to-Classical Coexistence: Wavefunction Decay Kinetics, Photon Entanglement, and Q-Bits
by Piero Chiarelli
Symmetry 2023, 15(12), 2210; https://doi.org/10.3390/sym15122210 - 18 Dec 2023
Cited by 2 | Viewed by 902
Abstract
By utilizing a generalized version of the Madelung quantum hydrodynamic framework that incorporates noise, we derive a solution using the path integral method to investigate how a quantum superposition of states evolves over time. This exploration seeks to comprehend the process through which [...] Read more.
By utilizing a generalized version of the Madelung quantum hydrodynamic framework that incorporates noise, we derive a solution using the path integral method to investigate how a quantum superposition of states evolves over time. This exploration seeks to comprehend the process through which a stable quantum state emerges when fluctuations induced by the noisy gravitational background are present. The model defines the conditions that give rise to a limited range of interactions for the quantum potential, allowing for the existence of coarse-grained classical descriptions at a macroscopic level. The theory uncovers the smallest attainable level of uncertainty in an open quantum system and examines its consistency with the localized behavior observed in large-scale classical systems. The research delves into connections and similarities alongside other theories such as decoherence and the Copenhagen foundation of quantum mechanics. Additionally, it assesses the potential consequences of wave function decay on the measurement of photon entanglement. To validate the proposed theory, an experiment involving entangled photons transmitted between detectors on the moon and Mars is discussed. Finally, the findings of the theory are applied to the creation of larger Q-bit systems at room temperatures. Full article
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