Operational characterization of general quantum correlation via complex weak value measurement

Abstract

The last two decades have witnessed significant progress on the understanding the quantum correlation more general than entanglement, wherein even a separable state may yield correlation that cannot be emulated by any classical object. Such a general nonclassical correlation is not only intriguing from the fundamental point of view, but it has also been recognized as a resource in a variety of quantum information processing tasks and quantum technology. Here, we propose a characterization of the general quantum correlation in bipartite system in terms of direct laboratory operations using weak measurement with postselection. We define a quantity based on the imaginary part of weak values obtained via weak measurement of a local basis followed by a postselection of another local basis, and an optimization procedure over all possible choices of the two bases. We show that it satisfies certain desirable requirements for a quantifier of general quantum correlations. It may be statistically interpreted as the minimum genuine quantum share of uncertainty. It is a faithful witness of entanglement for general pure states, giving an observable lower bound to a scaled square root of the linear entropy of entanglement. We then suggest an information theoretic interpretation of the general quantum correlation in a multipartite state as the minimum mean absolute error in an optimal estimation of any local measurement basis, based on the outcomes of local projective measurement on the state, in the worst case scenario.