Correlations in quantum states and the local creation of quantum discord

Quantum discord is usually referred to as a measure for quantum correlations. In the search of the fundamental resource to gain a quantum advantage in quantum information applications, quantum discord is considered a promising candidate. In this paper we present an alternative view on quantum correlations in terms of the rank of the correlation matrix as introduced by Dakić, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)]. According to our analysis, information about the quantum discord does not necessarily determine the amount of quantum correlations but rather the quantumness of the state. Nonzero quantum discord is only a necessary but not a sufficient condition for correlations above the classically achievable limit. This becomes clear when we consider states of nonzero discord, which can be created from zero discord states only by a single local operation. We further show that the set of these states has measure zero.

Figure 1

Schematic picture of the set of quantum states, classified by their quantum correlations, which are characterized by the two quantities $\mathcal{D}$ (discord) and $L$. The correlations of the state are identified by $L$, whereas the quantum nature is indicated by $\mathcal{D}$. In order to have correlations above the classical upper limit of $d_{\min }$, a nonzero value of $\mathcal{D}$ is required. The square on the bottom left represents the set of classical (zero discord) states. All of them have $L⩽d_{\min }$. The top right square depicts the set of quantum correlated states in terms of $L$, since $L>d_{\min }$. The bottom right square contains all states of nonzero discord but with low correlations, $L⩽d_{\min }$. A subset of these, indicated by a dotted area, can be reached by local operations (LO) from the set of classical states.