scholarly journals A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1190
Author(s):  
Liang Liu ◽  
Jinchuan Hou ◽  
Xiaofei Qi
Keyword(s):  
Quantum Correlation ◽  
Quantum Discord ◽  
Continuous Variable ◽  
Gaussian State ◽  
Product State ◽  
Gaussian States ◽  
System A ◽  
Gaussian Channels ◽  
The Mean ◽  
Gaussian Quantum Discord

Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

scholarly journals Quantum Correlation Based on Uhlmann Fidelity for Gaussian States

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 6
Author(s):  
Liang Liu ◽  
Jinchuan Hou ◽  
Xiaofei Qi
Keyword(s):  
Quantum Channel ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Gaussian States ◽  
Gaussian Quantum Discord ◽  
Geometric Measurement ◽  
Thermal States

A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states.

scholarly journals Fidelity-based unitary operation-induced quantum correlation for continuous-variable systems

2019 ◽  
Vol 17 (04) ◽  
pp. 1950035
Author(s):  
Liang Liu ◽  
Xiaofei Qi ◽  
Jinchuan Hou
Keyword(s):  
Quantum Correlation ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Gaussian Channel ◽  
Simple Computation ◽  
Gaussian States ◽  
Text Mode ◽  
Computation Formula ◽  
Geometric Measurement ◽  
Thermal States

We propose a measure of nonclassical correlation [Formula: see text] in terms of local Gaussian unitary operations based on square of the fidelity [Formula: see text] for bipartite continuous-variable systems. This quantity is easier to be calculated or estimated and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of [Formula: see text] for any [Formula: see text]-mode Gaussian states is presented and an estimation of [Formula: see text] for any [Formula: see text]-mode Gaussian states is given. For any [Formula: see text]-mode Gaussian states, [Formula: see text] does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing [Formula: see text] in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that [Formula: see text] is much better in detecting quantum correlations of Gaussian states.

scholarly journals GAUSSIAN GEOMETRIC DISCORD

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1773-1786 ◽  
Author(s):  
GERARDO ADESSO ◽  
DAVIDE GIROLAMI
Keyword(s):  
Quantum Discord ◽  
Gaussian Quadrature ◽  
Continuous Variable ◽  
Upper And Lower Bounds ◽  
Gaussian States ◽  
Physical Constraints ◽  
Geometric Measure ◽  
Classical Correlations ◽  
Qubit States ◽  
Thermal States

We extend the geometric measure of quantum discord, introduced and computed for two-qubit states, to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.

scholarly journals THE BALANCE OF QUANTUM CORRELATIONS FOR A CLASS OF FEASIBLE TRIPARTITE CONTINUOUS VARIABLE STATES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345024 ◽  
Author(s):  
STEFANO OLIVARES ◽  
MATTEO G. A. PARIS
Keyword(s):  
Conservation Laws ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Noisy Environment ◽  
Mixed States ◽  
Von Neumann ◽  
Entanglement Of Formation ◽  
Pure States ◽  
Gaussian Quantum Discord

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi–Winter-like conservation laws involving Gaussian entanglement of formation (EoF), Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.

scholarly journals Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 586 ◽  
Author(s):  
Julio López-Saldívar ◽  
Margarita Man’ko ◽  
Vladimir Man’ko
Keyword(s):  
Differential Equations ◽  
Quadratic Forms ◽  
Frequency Converter ◽  
Continuous Variable ◽  
Variable Density ◽  
Gaussian State ◽  
Density Matrices ◽  
Mean Values ◽  
Invariant States ◽  
The Mean

In the differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and momentum operators or quadrature components. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state, unitarily evolving according to a Hamiltonian H ^ . We also present the corresponding differential equations, which describe the nonunitary evolution of the subsystems. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schrödinger equation. The formalism elaborated allows us to define new specific invariant and quasi-invariant states, as well as states with invariant covariance matrices, i.e., states were only the mean values evolve according to the classical Hamilton equations. By using density matrices in the position and in the tomographic-probability representations, we study examples of these properties. As examples, we present novel invariant states for the two-mode frequency converter and quasi-invariant states for the bipartite parametric amplifier.

scholarly journals Continuous Variable Quantum Information: Gaussian States and Beyond

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440001 ◽  
Author(s):  
Gerardo Adesso ◽  
Sammy Ragy ◽  
Antony R. Lee
Keyword(s):  
Quantum Information ◽  
Symplectic Geometry ◽  
Quantum Information Processing ◽  
Mathematical Structure ◽  
Continuous Variable ◽  
Gaussian State ◽  
Mathematical Framework ◽  
Gaussian States ◽  
Subject Material ◽  
Selection Of

The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In this paper, we provide a brief, and hopefully didactic, exposition of Gaussian state quantum information and its contemporary uses, including sometimes omitted crucial details. After introducing the subject material and outlining the essential toolbox of continuous variable systems, we define the basic notions needed to understand Gaussian states and Gaussian operations. In particular, emphasis is placed on the mathematical structure combining notions of algebra and symplectic geometry fundamental to a complete understanding of Gaussian informatics. Furthermore, we discuss the quantification of different forms of correlations (including entanglement and quantum discord) for Gaussian states, paying special attention to recently developed measures. The paper is concluded by succinctly expressing the main Gaussian state limitations and outlining a selection of possible future lines for quantum information processing with continuous variable systems.

Quantum Discord of Two Bosonic Modes in Two-Reservoir Model

2013 ◽  
Vol 20 (03) ◽  
pp. 1340003 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Quantum Discord ◽  
Open Systems ◽  
Vacuum State ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Reservoir Model ◽  
Bipartite State ◽  
Thermal Environments ◽  
Gaussian Input ◽  
Gaussian Quantum Discord

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable quantum discord for a system consisting of two non-interacting bosonic modes embedded in two independent thermal environments. We describe the evolution of discord in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed vacuum state, we analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal reservoirs. For an initial separable pure state, the Gaussian quantum discord is zero and it keeps this value during the whole evolution of the system.

Dynamic of the Gaussian quantum discord and effect of non-Markovian degree

2015 ◽  
Vol 93 (4) ◽  
pp. 481-485
Author(s):  
Xin Liu ◽  
Wei Wu ◽  
Changkui Hu
Keyword(s):  
Markov Process ◽  
Experimental Method ◽  
Dynamic Characteristic ◽  
Quantum Discord ◽  
Thermal State ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Zero Temperature ◽  
The Relationship ◽  
Gaussian Quantum Discord

We study the dynamic of the Gaussian quantum discord in a continuous-variable system subject to a common non-Markovian environment with zero-temperature. By considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that Gaussian discord has a very different dynamic characteristic in a non-Markovian evolution versus a Markov process, and can be created by the memory effect, which features non-Markovianity. We also study the relationship between Gaussian discord and the non-Markovian degree of the environment. The results may offer us an effective experimental method to get more quantum correlations.

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