Quantum Markov chains, sufficiency of quantum channels, and Renyi information measures

摘要: A short quantum Markov chain is a tripartite state $\rho_{ABC}$ such that system $A$ can be recovered perfectly by acting on $C$ of the reduced $\rho_{BC}$. Such states have conditional mutual information $I(A;B|C)$ equal to zero and are only with this property. channel $\mathcal{N}$ sufficient for two $\rho$ $\sigma$ if there exists recovery using which one recover from $\mathcal{N}(\rho)$ $\mathcal{N}(\sigma)$. The relative entropy difference $D(\rho\Vert\sigma)-D(\mathcal{N}(\rho)\Vert\mathcal{N}(\sigma))$ $\sigma$. In paper, we show these properties extend Renyi generalizations measures were proposed in [Berta et al., J. Math. Phys. 56, 022205, (2015)] [Seshadreesan 48, 395303, (2015)], thus providing an alternate characterization chains channels. These results give further support quantities as being legitimate difference. Along way, solve some open questions Ruskai Zhang, regarding trace particular matrices arise study monotonicity under operations strong subadditivity von Neumann entropy.