The entropy power inequality with quantum conditioning

The conditional entropy power inequality is a fundamental inequality in information theory, stating
that the conditional entropy of the sum of two conditionally independent vector-valued random
variables each with an assigned conditional entropy is minimum when the random variables are
Gaussian. We prove the conditional entropy power inequality in the scenario where the conditioning
system is quantum. The proof is based on the heat semigroup and on a generalization of the Stam
inequality in the presence of quantum conditioning. The entropy power inequality with quantum
conditioning will be a key tool of quantum information, with applications in distributed source
coding protocols with the assistance of quantum entanglement.

Article web page: