2016/08/29 by Boyer, Michel
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1608.08136
The "classical-quantum" (cq) discord of a bipartite state ρAB is the smallest difference between the mutual information S(ρA:B) of ρ and that of ρ 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 ∑i pi |i⟩⟨ i|⊗ ρBi for pi a probability distribution, |i⟩ a basis of the A system and ρBi 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.