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Communications in Theoretical Physics

Quantum Correlations in Werner Derivatives

Sheng-Fang Wang, Yimin Liu, Guofeng Li, Xiansong Liu, Zhanjun Zhang

Published Oct 1, 2013• 1 citation
Publisher

Abstract

Quantum correlations in Werner derivatives are studied with two different approaches, i.e., measurement-induced disturbance (MID) [ Phys. Rev. A 77 (2008) 022301 ] and ameliorated MID (AMID) [ J. Phys. A 44 (2011) 352002 ]. They are derived via strict deductions with MID while numerically calculated via the measurement optimization with AMID. Interestingly, quantum correlations captured with both approaches are completely coincident. Moreover, some distinct features of the quantum correlations and their underlying physics are exposed via analyses and discussions.

DOI
10.1088/0253-6102/60/4/04

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Quantum correlations in Werner derivatives are studied with two different approaches, i.e., measurement-induced disturbance (MID) [ Phys. Rev. A 77 (2008) 022301 ] and ameliorated MID (AMID) [ J. Phys. A 44 (2011) 352002 ]. They are derived via strict deductions with MID while numerically calculated via the measurement optimization with AMID. Interestingly, quantum correlations captured with both approaches are completely coincident. Moreover, some distinct features of the quantum correlations and their underlying physics are exposed via analyses and discussions.
Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four different approaches, namely, quantum discord [Phys. Rev. Lett. 88 (2002) 017901], measurement-induced disturbance (MID) [ Phys. Rev. A 77 (2008) 022301 ], ameliorated MID [ J. Phys. A: Math. Theor. 44 (2011) 352002 ] and quantum dissonance [ Phys. Rev. Lett. 104 (2010) 080501 ]. Quantum correlations captured with different approaches are compared and discussed so that their three distinct features are exposed.
We study quantum correlations beyond entanglement in two-mode Gaussian states of continuous-variable systems by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two-mode Gaussian states comprising pure states where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two-mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong similarity with the case of two qubits. Upper and lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We further present a comparison between Gaussian AMID and Gaussian entanglement of formation, and classify families of two-mode states in terms of their Gaussian AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings provide a further confirmation of the genuinely quantum nature of general Gaussian states, yet they reveal that non-Gaussian measurements can play a crucial role for the optimized extraction and potential exploitation of classical and nonclassical correlations in Gaussian states.
Quantum correlations in a family of bipartite separable qubit-qutrit quantum-classical correlated states are investigated by using two popular measures, i.e., the original quantum discord (OQD) method by Ollivier and Zurek [ Phys. Rev. Lett. 88 (2001) 017901 ] and the measurement-induced disturbance (MID) method by Luo [ Phys. Rev. A 77 (2008) 022301 ]. It is found that both of them are functions of a parameter partially characterizing the concerned states, however, quantum correlations evaluated via the convenient MID method are somewhat overestimated.