The Entropy Power Inequality with quantum conditioning

Abstract

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.

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Cited by in corpus (7)

• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• From Rényi Entropy Power to Information Scan of Quantum States
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory