The multi-mode quantum Entropy Power Inequality

Abstract

The quantum version of a fundamental entropic data-processing inequality is presented. It establishes a lower bound for the entropy that can be generated in the output channels of a scattering process, which involves a collection of independent input bosonic modes (e.g., the modes of the electromagnetic field). The impact of this inequality in quantum information theory is potentially large and some relevant implications are considered in this work.

arXiv comment7 pages, 1 figure

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• Gaussian states minimize the output entropy of one-mode quantum Gaussian channels
• Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator
• 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
• Geometric inequalities from phase space translations
• Passive states as optimal inputs for single-jump lossy quantum channels
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Quantum-optical channels that output only classical states
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• The Entropy Power Inequality with quantum conditioning
• Conditional quantum entropy power inequality for $d$-level quantum systems
• Thinning, photonic beamsplitting, and a general discrete entropy power inequality
• From Rényi Entropy Power to Information Scan of Quantum States
• Uncertainty relations with quantum memory for the Wehrl entropy
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Quantifying coherence with quantum addition