Zero discord implies classicality

Abstract

The "classical-quantum" ($cq$) discord of a bipartite state ${\rho }^{AB}$ is the smallest difference between the mutual information $S({\rho }^{A:B})$ of $\rho$ and that of $\rho$ after a measurement channel is applied on the $A$ system. Relating zero discord to the strong subadditivity of the Von Neumann entropy, Datta proved that a state has zero $cq$ discord iff and only if it can be written in the form ${\sum }_i{p}_i|i⟩⟨i|\otimes {\rho }_i^B$ for $p_i$ a probability distribution, $|i⟩$ a basis of the $A$ system and ${\rho }_i^B$ states of the $B$ system. We provide a simple proof of that same result using directly a theorem of Petz on channels that leave unchanged the relative entropy of two given states.

Cited by in corpus (1)

• Entanglement and deterministic quantum computing with one qubit