A Measure for Quantum Correlation

Chang‐shui Yu, Haiqing Zhao

The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present a direct measure of quantum correlation by revealing the difference between the structures of classically and quantum correlated states. Our measure explicitly includes the contributions of the inseparability and local nonorthogonality of the eigenvectors of a density matrix. Besides its relatively easy computability, our measure can provide a unified understanding of quantum correlation of all the present versions.

Davide Girolami, Gerardo Adesso

Hui Cao, Zhao-Qin Wu, Liyun Hu +2 more

To measure the quantum correlation of a bipartite state, a test matrix is constructed through the commutations among the blocks of its density matrix, which turns out to be a zero matrix for a classical state with zero quantum correlation, and a nonzero one for a quantum state with positive quantum correlation. The Frobenius norm of the test matrix is used to measure the quantum correlation, which satisfies the basic requirements for a good measure and coincides with Wootters concurrence for two-qubit pure states. Since no optimization is involved in the definition, this measure of quantum correlation is easy to compute and even can be calculated manually.

Gerardo Adesso, Davide Girolami

I.-O. Stamatescu

Aharon Brodutch, Kavan Kishore Modi

Entanglement does not describe all quantum correlations and several authors have shown the need to go beyond entanglement when dealing with mixed states. Various different measures have sprung up in the literature, for a variety of reasons, to describe bipartite and multipartite quantum correlations; some are known under the collective name {\it quantum discord}. Yet, in the same sprit as the criteria for entanglement measures, there is no general mechanism that determines whether a measure of quantum and classical correlations is a proper measure of correlations. This is partially due to the fact that the answer is a bit muddy. In this article we attempt tackle this muddy topic by writing down several criteria for a ``good" measure of correlations. We breakup our list into \emph{necessary}, \emph{reasonable}, and \emph{debatable} conditions. We then proceed to prove several of these conditions for generalized measures of quantum correlations. However, not all conditions are met by all measures; we show this via several examples. The reasonable conditions are related to continuity of correlations, which has not been previously discussed. Continuity is an important quality if one wants to probe quantum correlations in the laboratory. We show that most types of quantum discord are continuous but none are continuous with respect to the measurement basis used for optimization.