Pairwise correlations via quantum discord and its geometric measure in a four-qubit spin chain

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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Tight lower bound to the geometric measure of quantum discord

Physical Review A ◽

10.1103/physreva.85.024302 ◽

2012 ◽

Vol 85 (2) ◽

Cited By ~ 55

Author(s):

Ali Saif M. Hassan ◽

Behzad Lari ◽

Pramod S. Joag

Keyword(s):

Lower Bound ◽

Quantum Discord ◽

Geometric Measure

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QUANTUM CORRELATIONS IN THE "q-DEFORMED" WERNER STATE

International Journal of Quantum Information ◽

10.1142/s0219749913500184 ◽

2013 ◽

Vol 11 (02) ◽

pp. 1350018 ◽

Cited By ~ 2

Author(s):

BO LIU ◽

KANG XUE ◽

GANGCHENG WANG ◽

CHUNFANG SUN ◽

LIDAN GOU ◽

...

Keyword(s):

Quantum Discord ◽

Singlet State ◽

Great Influence ◽

Quantum Correlations ◽

Werner State ◽

Single Loop ◽

Geometric Measure ◽

Topological Parameter ◽

Spin Singlet ◽

Two Parameters

We investigate quantum discord of the "q-deformed" Werner state via Yang–Baxterization approach. There are two parameters q and u in this "q-deformed" Werner state. The parameter u, which plays an important role in some typical models, is related to the probability of the "q-deformed" two-qubit spin singlet state in this study. The "q-deformed" parameter q is related to the single loop through d = q + q-1. When topological parameter d approaches 2 (i.e. q → 1), the "q-deformed" Werner state degenerates into the well-known Werner state. The results show that topological parameter d has great influence on quantum correlations of the "q-deformed" Werner state. When we fix the parameter u, the quantum correlations decrease with increasing the single loop d. When d approaches +∞ (i.e. q → 0+ or +∞), quantum discord, geometric measure of quantum discord and entanglement all tend to 0. While d approaches 2 (i.e. q → 1), all of them just have the same results with the Werner state.

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Effects of phase shift on bipartite and multipartite correlations of a spin chain under dephasing

Open Physics ◽

10.1515/phys-2015-0025 ◽

2015 ◽

Vol 13 (1) ◽

Author(s):

Ai-Xi Chen ◽

Jian-Song Zhang

Keyword(s):

Steady State ◽

Phase Shift ◽

Analytical Solution ◽

Spin Chain ◽

Quantum Discord ◽

Present Model ◽

Spin Squeezing ◽

Heisenberg Chain ◽

Initial Correlations ◽

Long Time

AbstractWe investigate the effects of phase shift on entanglement, quantum discord, geometric discord, and spinsqueezing of a Heisenberg chain under dephasing. An analytical solution of the present model is obtained. Our results show that the initial correlations of the spin chain could be partially stored for a long time in the presence of dephasing and the amount of steady state correlations can be adjusted via phase shift. Particularly, we find the effects of phase shift on quantum discord and geometric discord are not always the same, i.e., the increase of geometric discord does not always imply the increase of quantum discord. Then, we calculate the spin-squeezing of the spin chain and find that spin-squeezing first increases with time and then reaches a plateau. The amount of spin-squeezing can be controlled via phase shift.

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Quantum Discord in Photon-Added Glauber Coherent States of GHZ-Type

Open Systems & Information Dynamics ◽

10.1142/s1230161215500237 ◽

2015 ◽

Vol 22 (04) ◽

pp. 1550023

Author(s):

M. Daoud ◽

W. Kaydi ◽

H. El Hadfi

Keyword(s):

Coherent States ◽

Quantum Discord ◽

Quantum Correlations ◽

Photon Excitation ◽

Pairwise Correlations ◽

Photon Excitations

We investigate the influence of photon excitations on quantum correlations in tripartite Glauber coherent states of Greenberger-Horne-Zeilinger type (GHZ-type). The pairwise correlations are measured by means of the entropy-based quantum discord. We also analyze the monogamy property of quantum discord in this class of tripartite states in terms of the strength of Glauber coherent states and the photon excitation order.

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