Quantum correlations in Gaussian states via Gaussian channels: steering, entanglement, and discord

2016 ◽  
Vol 15 (6) ◽  
pp. 2441-2453 ◽  
Author(s):  
Zhong-Xiao Wang ◽  
Shuhao Wang ◽  
Qiting Li ◽  
Tie-Jun Wang ◽  
Chuan Wang
Keyword(s):  
Quantum Correlations ◽  
Gaussian States ◽  
Gaussian Channels

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 States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

2017 ◽  
Vol 118 (16) ◽  
Author(s):  
Giacomo De Palma ◽  
Dario Trevisan ◽  
Vittorio Giovannetti
Keyword(s):  
Gaussian States ◽  
Gaussian Channels ◽  
Output Entropy

scholarly journals A field theory study of entanglement wedge cross section: odd entropy

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Ali Mollabashi ◽  
Kotaro Tamaoka
Keyword(s):  
Cross Section ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Scale Invariant ◽  
Gaussian States ◽  
Von Neumann ◽  
Free Scalar ◽  
The Difference

Abstract We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to Gaussian states of scale-invariant theories as well as their finite temperature generalizations, for which we show that odd entropy is a well-defined measure for mixed states. Motivated from holographic results, the difference between odd and von Neumann entropy is also studied. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy, which is qualitatively consistent with the holographic CFT. In general cases, we also find that this difference is not even a monotonic function with respect to size of (and distance between) subsystems.

scholarly journals ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 383-393 ◽  
Author(s):  
GERARDO ADESSO ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Tripartite Entanglement ◽  
Gaussian States ◽  
Trade Off ◽  
Entanglement Sharing

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

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.

INTERFERENCE OF MULTI-MODE GAUSSIAN STATES AND "NON APPEARANCE" OF QUANTUM CORRELATIONS

2012 ◽  
Vol 10 (08) ◽  
pp. 1241004 ◽  
Author(s):  
STEFANO OLIVARES
Keyword(s):  
Beam Splitter ◽  
Quantum Correlations ◽  
Gaussian States ◽  
Multi Mode ◽  
Mode Mixing

We theoretically investigate bilinear, mode-mixing interactions involving two modes of uncorrelated multi-mode Gaussian states. In particular, we introduce the notion of "locally the same states" (LSS) and prove that two uncorrelated LSS modes are invariant under the mode mixing, i.e. the interaction does not lead to the birth of correlations between the outgoing modes. We also study the interference of orthogonally polarized Gaussian states by means of an interferometric scheme based on a beam splitter, rotators of polarization and polarization filters.

DYNAMICS OF QUANTUM CORRELATIONS OF TWO INTERFERING BIPARTITE GAUSSIAN STATES

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1727-1736
Author(s):  
STEFANO OLIVARES
Keyword(s):  
Phase Space ◽  
Beam Splitter ◽  
Quantum Correlations ◽  
Gaussian States ◽  
Phase Space Analysis ◽  
Space Analysis

We address the interference of a pair of two-mode Gaussian states, interacting pairwise through a beam-splitter Hamiltonian. In the framework of a suitable phase-space analysis, the correlations generated through the interaction are studied by considering a quantity proportional to the variance of difference between the detected photocurrents of all the possible couples of modes. We use this quantity to demonstrate the invariance through the interaction and the correlations swapping also in the presence of nonideal photodetection.

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