Quantifying non-classicality with local unitary operations

Abstract

We propose a measure of non-classical correlations in bipartite quantum states based on local unitary operations. We prove the measure is non-zero if and only if the quantum discord is non-zero; this is achieved via a new characterization of zero discord states in terms of the state's correlation matrix. Moreover, our scheme can be extended to ensure the same relationship holds even with a generalized version of quantum discord in which higher-rank projective measurements are allowed. We next derive a closed form expression for our scheme in the cases of Werner states and (2 x N)-dimensional systems. The latter reveals that for (2 x N)-dimensional states, our measure reduces to the geometric discord [Dakic et al., PRL 105, 2010]. A connection to the CHSH inequality is shown. We close with a characterization of all maximally non-classical, yet separable, (2 x N)-dimensional states of rank at most two (with respect to our measure).