Chain Rule for the Quantum Relative Entropy
Kun Fang, Omar Fawzi, Renato Renner, David Sutter
Abstract
The chain rule for the classical relative entropy ensures that the relative entropy between probability distributions on multipartite systems can be decomposed into a sum of relative entropies of suitably chosen conditional distributions on the individual systems. Here, we prove a chain rule inequality for the quantum relative entropy. The new chain rule allows us to solve an open problem in the context of asymptotic quantum channel discrimination: surprisingly, adaptive protocols cannot improve the error rate for asymmetric channel discrimination compared to nonadaptive strategies.
Topics & Concepts
Kullback–Leibler divergenceGeneralized relative entropyStatistical physicsQuantum relative entropyMultipartiteConditional entropyChain rule (probability)QuantumJoint quantum entropyEntropy (arrow of time)Quantum discordMathematicsConditional quantum entropyComputer scienceProbability distributionPrinciple of maximum entropyQuantum mechanicsPhysicsMaximum entropy thermodynamicsQuantum entanglementStatisticsRegular conditional probabilityProbability mass functionQuantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems