Geometric measure of quantum discord in non-Markovian environments

2010 ◽  
Vol 283 (24) ◽  
pp. 5264-5268 ◽  
Author(s):  
Ferdi Altintas
Keyword(s):  
Quantum Discord ◽  
Geometric Measure

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 Tight lower bound to the geometric measure of quantum discord

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
Ali Saif M. Hassan ◽  
Behzad Lari ◽  
Pramod S. Joag
Keyword(s):  
Lower Bound ◽  
Quantum Discord ◽  
Geometric Measure

QUANTUM CORRELATIONS IN THE "q-DEFORMED" WERNER STATE

2013 ◽  
Vol 11 (02) ◽  
pp. 1350018 ◽  
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.

Evaluating the geometric measure of quantum discord

2012 ◽  
Vol 171 (3) ◽  
pp. 870-878 ◽  
Author(s):  
Shunlong Luo ◽  
Shuangshuang Fu
Keyword(s):  
Quantum Discord ◽  
Geometric Measure

The renormalization of geometric quantum discord in the transverse Ising model

2015 ◽  
Vol 29 (03) ◽  
pp. 1550002 ◽  
Author(s):  
Xiu-Xing Zhang ◽  
Hong-Rong Li
Keyword(s):  
Ising Model ◽  
Critical Point ◽  
Ground State ◽  
Quantum Discord ◽  
Recurrence Relations ◽  
Sudden Change ◽  
System Size ◽  
Transverse Ising Model ◽  
Geometric Measure ◽  
First Derivative

Using the quantum renormalization group (QRG) method, we investigate the ground state geometric measure of quantum discord (GQD) of the transverse Ising model. The analytical expression of GQD together with the RG recurrence relations are obtained. The critical and scaling behaviors of GQD are investigated. Our results show that with the increasing of RG steps, GQD (first derivative of GQD) exhibits sudden change (dip) in behavior at the critical point, which indicates that the system undergoes phase transitions between the Ising and the paramagnetic phases. The critical exponent that governs the divergences of the first derivative of GQD is calculated. How the critical point of the model is approached as the increasing of the system size is revealed.

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