Geometric Measure Of Quantum Discord Research Articles

Quantum Discord of Two-Qubit Thermal State in Hydrogen Atom

The geometric measure of quantum discord (GMQD) is used to study the quantum correlation in a two-qubit thermal state in hydrogen atom. External magnetic field can destroy the initial symmetry of the state and further change its degeneracy structure. The dependence of the quantum correlation on temperature and magnetic field is discussed.

Quantum correlations in spin models

Bell nonlocality, entanglement and nonclassical correlations are different aspects of quantum correlations for a given state. There are many methods to measure nonclassical correlations. In this paper, nonclassical correlations in two-qubit spin models are measured by the use of measurement-induced disturbance (MID) [S. Luo, Phys. Rev. A 77 (2008) 022301] and geometric measure of quantum discord (GQD) [B. Dakić, V. Vedral, C. Brukner, Phys. Rev. Lett. 105 (2010) 190502]. Their dependences on external magnetic field, spin–spin coupling, and the Dzyaloshinskii–Moriya (DM) interaction are presented in detail. We also compare Bell nonlocality, entanglement measured by concurrence, MID and GQD and illustrate their different characteristics.

Measurement-Induced Nonlocality

We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.

Geometric measure of quantum discord under decoherence

The dynamics of a geometric measure of the quantum discord (GMQD) under decoher-ence is investigated. We show that the GMQD of a two-qubit state can be alternativelyobtained through the singular va...

Geometric measure of quantum discord under decoherence

The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a $3\times4$ matrix whose elements are the expectation values of Pauli matrices of the two qubits. By using Heisenberg picture, the analytic results of the GMQD is obtained for three typical kinds of the quantum decoherence channels. We compare the dynamics of the GMQD with that of the quantum discord and of entanglement. We show that a sudden change in the decay rate of the GMQD does not always imply that of the quantum discord, and vice versa. We also give a general analysis on the sudden change in behavior and find that at least for the Bell diagonal states, the sudden changes in decay rates of the GMQD and that of the quantum discord occur simultaneously.

Geometric measure of quantum discord

Dakic, Vedral, and Brukner [arXiv:1004.0190 (2010)] introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. This measure is significant in capturing quantum correlations from a geometric perspective. In this brief report, we evaluate the geometric measure of quantum discord for an arbitrary state and obtain an explicit and tight lower bound. Furthermore, we reveal an intrinsic feature of geometric measure of quantum discord by showing that it actually coincides with a simpler quantity based on von Neumann measurements.

Geometric measure of quantum discord in non-Markovian environments

We study the dynamics of geometric measure of quantum discord between two non-interacting qubits each immersed in its own non-Markovian environment with a spectal distribution representing the electromagnetic field inside off-resonant high-Q cavity. We compared the dynamics of geometric measure of quantum discord with quantum discord for an initial Werner-like state and conclude three important findings. First, when there is an instantaneous disappearance in the dynamics of quantum discord at some timepoints, there is a disappearance in geometric measure of quantum discord, but not instantly. Second, the sudden change in the decay rate of geometric measure of quantum discord might not imply the sudden change in the decay rate of the dynamics of quantum discord. Third, there is a preservation for a long time in both quantum discord and geometric measure of quantum discord when the detuning and non-Markovian conditions are simultaneously satisfied.