Discord vs Distortion: Classical vs Quantum

Quantum discord is a popular quantum-resource measure but a nonzero value does not necessarily imply quantumness; nonzero classical discord arises if local measurements disturb the stochastic information state [V. Gheorghiu, M. C. de Oliveira and B. C. Sanders, Phys. Rev. Lett. 115, 030403 (2015)]. The classical interpretation of discord breaks down if and only if entanglement of formation for the informational state is nonzero, thereby creating a tight link between entanglement and genuine quantum discord. Here we present mathematical relations, and specifically monotonicity between discord and channel-distortion measures such as mean-squared distortion and Kullback-Leibler divergence. Whereas the previous result showed discord can be nonzero for stochastic information, our new results demonstrate a tight link between classical discord and other information-theoretic measures of noisy channels.