The conditional entropy power inequality for quantum additive noise channels
Abstract
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional Entropy Power Inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional Entropy Power Inequality to find an array of informationtheoretic inequalities for conditional entropies which are the analogues of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum OrnsteinUhlenbeck semigroup based on Entropy Power Inequalities.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 December 2018
 DOI:
 10.1063/1.5027495
 arXiv:
 arXiv:1803.00470
 Bibcode:
 2018JMP....59l2201D
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory;
 Mathematical Physics
 EPrint:
 26 pages