The conditional entropy power inequality for Gaussian quantum states

Abstract

We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.

27 pages, 4 figures

References in corpus (5)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Quantum Communication With Zero-Capacity Channels
• The entropy power inequality for quantum systems
• Limits on classical communication from quantum entropy power inequalities
• Schemes of transmission of classical information via quantum channels with many senders: discrete and continuous variables cases

Cited by in corpus (26)

• The conditional Entropy Power Inequality for bosonic quantum systems
• Entropy power inequalities for qudits
• Gaussian optimizers for entropic inequalities in quantum information
• The conditional entropy power inequality for quantum additive noise channels
• Bosonic quantum communication across arbitrarily high loss channels
• Geometric inequalities from phase space translations
• Derivatives of symplectic eigenvalues and a Lidskii type theorem
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• Quantum-optical channels that output only classical states
• Bounds on Information Combining With Quantum Side Information
• Upper bounds on the quantum capacity for general attenuator and amplifier
• The Entropy Power Inequality with quantum conditioning
• RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
• Refined diamond norm bounds on the emergence of objectivity of observables
• Conditional quantum entropy power inequality for $d$-level quantum systems
• Contractivity properties of a quantum diffusion semigroup
• Uncertainty relations with quantum memory for the Wehrl entropy
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• Upper bounds on the private capacity for bosonic Gaussian channels
• Universal upper bounds for Gaussian information capacity
• First order sensitivity analysis of symplectic eigenvalues
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory