Quantum Discord For Two-qubit States Research Articles

Geometric global quantum discord of two-qubit states**Project supported by the National Natural Science Foundation of China (Grant Nos. 11275131, 11305105, and 11271138) and Simons Foundation (Grant No. 198129).

We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.

Progress on Quantum Discord of Two-Qubit States: Optimization and Upper Bound

Calculation of the quantum discord requires to find the minimum of the quantum conditional entropy $S(\rho^{AB}|\{\Pi^B_{k}\})$ over all measurements on the subsystem $B$. In this paper, we provide a simple relation for the conditional entropy as the difference of two Shannon entropies. The relation is suitable for calculation of the quantum discord in the sense that it can by used to obtain the quantum discord for some classes of two-qubit states, without the need for minimization. We also present an analytical procedure of optimization and obtain conditions under which the quantum conditional entropy of a general two-qubit state is stationary. The presented relation is also used to find a tight upper bound on the quantum discord.

Optimal measurement for quantum discord of two-qubit states

We present an efficient method to solve the quantum discord of two-qubit X states exactly. A geometric picture is used to clarify whether and when the general POVM measurement is superior to von Neumann measurement. We show that either the von Neumann measurement or the three-element POVM measurement is optimal, and more interestingly, in the latter case the components of the postmeasurement ensemble are invariant for a class of states.

Dynamics of quantum discord under decoherence from a spin environment

The effect of decoherence from a spin environment on quantum discord of two-qubit states is investigated. Our results imply that the dynamics of quantum discord depend not only on the white noise in the Werner state, the coupling strength, and the number of the freedom degrees of the environment but also on the tunneling elements of the environment and the initial state of the environment. By a comparison, we find that the quantum discord for some unentangled states is not zero when the effect of the white noise on the quantum discord and entanglement is considered. With regard to the effect of other factors on the quantum discord and entanglement, we find that both of the quantum discord and entanglement take similar behaviors to a large extent.