scholarly journals IN THE CONTEXT OF TIME-INDEPENDENT PARAMETERS IN TWO QUANTUM SYSTEMS: QUANTUM ENTANGLEMENT AND CORRELATIONS WITH NEGATIVITY MEASUREMENT

2020 ◽  
pp. 316-327
Author(s):  
Rasim DERMEZ ◽  
Yilmaz TUNÇER
Keyword(s):  
Quantum Entanglement ◽  
Quantum Systems ◽  
Independent Parameters

scholarly journals Quantum Entanglement of Free Particles

2021 ◽  
Author(s):  
Roumen Tsekov
Keyword(s):  
Schrödinger Equation ◽  
Quantum Entanglement ◽  
Schrodinger Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Integral Of Motion ◽  
Friction Forces ◽  
Correlation Decay ◽  
Free Particles ◽  
Over Time

In this paper, the Schrödinger equation is solved for many free particles and their quantum entanglement is studied via correlation analysis. Converting the Schrödinger equation in the Madelung hydrodynamic-like form, the quantum mechanics is extended to open quantum systems by adding Ohmic friction forces. The dissipative evolution confirms the correlation decay over time, but a new integral of motion is discovered, being appropriate for storing everlasting quantum information.

Product-form monogamy relations of entanglement in multiqubit systems

2021 ◽  
pp. 2150022
Author(s):  
Jia-Bin Zhang ◽  
Tao Li ◽  
Zhi-Xi Wang
Keyword(s):  
Lower Bound ◽  
Quantum Entanglement ◽  
Quantum Systems ◽  
Product Form ◽  
Multipartite Entanglement ◽  
Multi Body ◽  
Monogamy Relations

Monogamy relations of entanglement play an important role in quantum systems, however, most of them are given in summation form. In this paper, we investigate the product-form monogamy relations of multipartite entanglement in terms of the [Formula: see text]th power of concurrence and negativity. Compared with the existing monogamy relations, the product-form monogamy relations of multi-body quantum entanglement have a stricter lower bound.

scholarly journals OPEN QUANTUM DYNAMICS: COMPLETE POSITIVITY AND ENTANGLEMENT

2005 ◽  
Vol 19 (19) ◽  
pp. 3063-3139 ◽  
Author(s):  
FABIO BENATTI ◽  
ROBERTO FLOREANINI
Keyword(s):  
Quantum Entanglement ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Complete Positivity ◽  
Information Communication ◽  
Open Quantum ◽  
Statistical Correlations ◽  
Quantum Open System ◽  
Algebraic Constraint

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behavior of bipartite systems immersed in the same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.

scholarly journals Signatures of Quantum Mechanics in Chaotic Systems

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 618 ◽  
Author(s):  
Kevin M. Short ◽  
Matthew A. Morena
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Chaotic Systems ◽  
Measurement Problem ◽  
Quantum Systems ◽  
Analytical Tool ◽  
Quantum Mechanical ◽  
Unstable Periodic Orbits ◽  
Classical Correspondence ◽  
Quantum Mechanical Systems

We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.

Exploring Chaos and Entanglement in the Hénon–Heiles System Using Squeezed Coherent States

2016 ◽  
Vol 26 (03) ◽  
pp. 1650052
Author(s):  
Sijo K. Joseph ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Quantum Entanglement ◽  
Local Structure ◽  
Coherent States ◽  
Quantum Systems ◽  
Initial Condition ◽  
Chaotic Orbit ◽  
Chaotic Orbits ◽  
Classical Correspondence ◽  
Squeezed Coherent State ◽  
Classical Phase Space

Quantum entanglement in the Hénon–Heiles system is analyzed using the squeezed coherent state. Enhancement of quantum entanglement via squeezing is explored in connection with chaotic and regular dynamics of the system. It is found that the entanglement enhancement via squeezing is implicitly linked to the local structure of the classical phase-space and it shows a clear quantum-classical correspondence. In particular, the entanglement enhancement via squeezing is found to be negligible for a highly chaotic orbit compared to the regular and weakly chaotic orbits, and shows a clear correspondence to the degree of chaos present in the classical initial condition. We believe that these results might be useful to develop efficient strategies to enhance entanglement in quantum systems.

Entanglement, Decoherence and Which-Path Information

2020 ◽  
pp. 124-139
Author(s):  
Gershon Kurizki ◽  
Goren Gordon
Keyword(s):  
Quantum Information ◽  
Free Will ◽  
Quantum Entanglement ◽  
Quantum Coherence ◽  
Life Forms ◽  
Quantum Systems ◽  
Quantum Computers ◽  
Classical Information ◽  
Composite Systems ◽  
Path Information

Henry attempts to sneak into Eve’s residence undetected by taking advantage of his quantum coherence, but his quantum entanglement with Schred puts him in peril: Henry can no longer interfere with himself, he decoheres, since his two versions are differently tagged by correlations with different versions of Schred. Entanglement in composite systems is not only the hallmark of quantumness but also the key to its demise, alias decoherence. Decoherence, by transforming quantum information into classical information, is the biggest obstacle towards controlling complex quantum systems, particularly quantum computers. Information is collected and processed by “observers”: all life forms and their artificial (computerized) extensions. The question that reflects the millennia-long controversy on free will is: do observers have the freedom to choose the mode of their observation? The appendix to this chapechapter investigates the interference of two quantum systems as a function of their entanglement.

scholarly journals Quantum Entanglement in Double Quantum Systems and Jaynes-Cummings Model

2017 ◽  
Vol 12 (1) ◽  
Author(s):  
Paweł Jakubczyk ◽  
Klaudiusz Majchrowski ◽  
Igor Tralle
Keyword(s):  
Quantum Entanglement ◽  
Quantum Systems ◽  
Double Quantum

scholarly journals A geometric Hamiltonian description of composite quantum systems and quantum entanglement

2015 ◽  
Vol 12 (07) ◽  
pp. 1550069 ◽  
Author(s):  
Davide Pastorello
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Quantum Entanglement ◽  
Hamiltonian Formulation ◽  
Classical Mechanics ◽  
Hamiltonian Formalism ◽  
Quantum Systems ◽  
Point Of View ◽  
Entanglement Measure ◽  
Hamiltonian Description

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.

scholarly journals Quantum Entanglement, Interaction, And The Classical Limit

2004 ◽  
Vol 59 (7-8) ◽  
pp. 425-436 ◽  
Author(s):  
Thomas Durt
Keyword(s):  
Wave Function ◽  
Quantum Entanglement ◽  
Classical Limit ◽  
Quantum Systems ◽  
Wave Functions ◽  
Bipartite System ◽  
Individual Wave

Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product states. Only when the systems are in a factorisable state they can be considered to be separated (in the sense of Bell). We show that whenever two quantum systems interact with each other, it is impossible that all factorisable states remain factorisable during the interaction unless the full Hamiltonian does not couple these systems so to say unless they do not really interact. We also present certain conditions under which particular factorisable states remain factorisable although they represent a bipartite system whose components mutually interact.We identify certain quasi-classical regimes that satisfy these conditions and show that they correspond to classical, pre-quantum, paradigms associated to the concept of particle. - PACS number: O3.65.Bz

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