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 information-theoretic 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 Ornstein-Uhlenbeck semigroup based on Entropy Power Inequalities.

arXiv comment26 pages; updated to match published version

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Cited by in corpus (15)

• The Quantum Wasserstein Distance of Order 1
• Learning quantum data with the quantum Earth Mover's distance
• Quantum optimal transport with quantum channels
• On contraction coefficients, partial orders and approximation of capacities for quantum channels
• Gaussian optimizers for entropic inequalities in quantum information
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• The Entropy Power Inequality with quantum conditioning
• Deviation bounds and concentration inequalities for quantum noises
• Upper bounds on the private capacity for bosonic Gaussian channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Energy preserving evolutions over Bosonic systems
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems