GAUSSIAN GEOMETRIC DISCORD

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.

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Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Open Systems & Information Dynamics ◽

10.1007/s11080-005-5730-2 ◽

2005 ◽

Vol 12 (02) ◽

pp. 189-205 ◽

Cited By ~ 22

Author(s):

Gerardo Adesso ◽

Alessio Serafini ◽

Fabrizio Illuminati

Keyword(s):

Tomographic Reconstruction ◽

Continuous Variable ◽

The State ◽

Upper And Lower Bounds ◽

Mixed States ◽

Gaussian States ◽

Pure States ◽

Classical Correlations ◽

Quantum And Classical Correlations

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.

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Quantum Correlation Based on Uhlmann Fidelity for Gaussian States

Entropy ◽

10.3390/e21010006 ◽

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.

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

International Journal of Quantum Information ◽

10.1142/s0219749919500357 ◽

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.

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ENTANGLEMENT CRITERION FOR COHERENT SUBTRACTION AND COHERENT ADDITION OF BIPARTITE CONTINUOUS VARIABLE STATES

International Journal of Quantum Information ◽

10.1142/s0219749913500603 ◽

2013 ◽

Vol 11 (06) ◽

pp. 1350060

Author(s):

LI-ZHEN JIANG ◽

XIAO-YU CHEN ◽

TIAN-YU YE ◽

FANG-YU HONG ◽

LIANG-NENG WU

Keyword(s):

Thermal Noise ◽

Photon Number ◽

Sufficient Conditions ◽

Continuous Variable ◽

Entangled State ◽

Gaussian States ◽

Non Gaussian ◽

Entanglement Criterion ◽

Entanglement Conditions ◽

Thermal States

We study the entanglement conditions of two quite general classes of two-mode non-Gaussian states. Using computable cross norm and realignment criterion, we obtain the sufficient conditions of entanglement for coherently added or subtracted two-mode squeezed thermal states, and the sufficient condition of entanglement for any photon number entangled state (PNES) evolving in a thermal noise and amplitude damping channel.

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Correlations in Two-Qubit Systems under Non-Dissipative Decoherence

Axioms ◽

10.3390/axioms9010020 ◽

2020 ◽

Vol 9 (1) ◽

pp. 20

Author(s):

Diego G. Bussandri ◽

Tristán M. Osán ◽

Pedro W. Lamberti ◽

Ana P. Majtey

Keyword(s):

Mutual Information ◽

Quantum Discord ◽

Quantum Correlations ◽

The Other ◽

Standard Quantum ◽

Optimal Value ◽

Quantum Mutual Information ◽

Classical Correlations ◽

Correlation Measures ◽

Qubit States

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.

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Studying quantum correlations dynamics in the phase space for continuous-variable Werner states and Bell-diagonal states

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819501093 ◽

2019 ◽

Vol 16 (07) ◽

pp. 1950109

Author(s):

Fatima-Zahra Siyouri ◽

Hicham Ait Mansour ◽

Fadoua Elbarrichi

Keyword(s):

Wigner Function ◽

Quantum Discord ◽

Open Quantum Systems ◽

Quantum Correlations ◽

Continuous Variable ◽

Quantum Systems ◽

Qubit System ◽

Classical Correlations ◽

Werner States ◽

System F

We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.

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CLASSICALITY WITNESS FOR TWO-QUBIT STATES

International Journal of Quantum Information ◽

10.1142/s0219749912500281 ◽

2012 ◽

Vol 10 (03) ◽

pp. 1250028 ◽

Cited By ~ 16

Author(s):

JONAS MAZIERO ◽

ROBERTO M. SERRA

Keyword(s):

Nuclear Magnetic Resonance ◽

Probability Distribution ◽

Quantum Discord ◽

Orthonormal Basis ◽

Broad Class ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Classical Correlations ◽

Necessary And Sufficient ◽

Qubit States

In the last few years one realized that if the state of a bipartite system can be written as ∑i,j pij|ai〉〈ai| ⊗ |bj〉〈bj|, where {|ai〉} and {|bj〉} form orthonormal basis for the subsystems and {pij} is a probability distribution, then it possesses at most classical correlations. In this article we introduce a nonlinear witness providing a sufficient condition for classicality of correlations (absence of quantum discord) in a broad class of two-qubit systems. Such witness turns out to be necessary and sufficient condition in the case of Bell-diagonal states. We show that the witness introduced here can be readily experimentally implemented in nuclear magnetic resonance setups.

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A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Entropy ◽

10.3390/e23091190 ◽

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.

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