Overcoming ambiguities in classical and quantum correlation measures

Abstract

We identify ambiguities in the available frameworks for defining quantum, classical, and total correlations as measured by discord-like quantifiers. More specifically, we determine situations for which either classical or quantum correlations are not uniquely defined due to degeneracies arising from the optimization procedure over the state space. In order to remove such degeneracies, we introduce a general approach where correlations are independently defined, escaping therefore from a degenerate subspace. As an illustration, we analyze the trace-norm geometric quantum discord for two-qubit Bell-diagonal states.