Quantifying nonclassicality with local unitary operations

Abstract

We propose a measure of nonclassical correlations in bipartite quantum states based on local unitary operations. We prove that the measure is nonzero if and only if the quantum discord is nonzero; 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 that 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 $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional systems. The latter reveals that for $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional states, our measure reduces to the geometric discord [Daki\ifmmode \acute{c}\else \'{c}\fi{} et al., Phys. Rev. Lett. 105, 190502 (2010)]. A connection to the Clauser-Horne-Shimony-Holt inequality is shown. We close with a characterization of all maximally nonclassical, yet separable, $(2\ifmmode\times\else\texttimes\fi{}N)$-dimensional states of rank at most 2 (with respect to our measure).