Overcoming ambiguities in classical and quantum correlation measures

TL;DR

This paper addresses ambiguities in quantum and classical correlation measures caused by degeneracies in optimization, proposing a new approach to define correlations independently and illustrating it with the trace-norm geometric quantum discord.

Contribution

The authors introduce a general method to resolve degeneracies in correlation measures by defining quantum and classical correlations independently.

Findings

Identified degeneracies in existing correlation measures.

Proposed a new approach to define correlations independently.

Analyzed trace-norm geometric quantum discord for Bell-diagonal states.

Abstract

We identify ambiguities in the available frameworks for defining quantum, classical, and total correlations as measured by discordlike 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.