Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator

Abstract

We prove that Gaussian thermal input states minimize the output von Neumann entropy of the one-mode Gaussian quantum-limited attenuator for fixed input entropy. The Gaussian quantum-limited attenuator models the attenuation of an electromagnetic signal in the quantum regime. The Shannon entropy of an attenuated real-valued classical signal is a simple function of the entropy of the original signal. A striking consequence of energy quantization is that the output von Neumann entropy of the quantum-limited attenuator is no more a function of the input entropy alone. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new isoperimetric inequality. Our result implies that geometric input probability distributions minimize the output Shannon entropy of the thinning for fixed input entropy. Moreover, our result opens the way to the multimode generalization, that permits to determine both the triple trade-off region of the Gaussian quantum-limited attenuator and the classical capacity region of the Gaussian degraded quantum broadcast channel.

References in corpus (7)

• Gaussian states in continuous variable quantum information
• Quantum thermodynamics of general quantum processes
• Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
• Limits on classical communication from quantum entropy power inequalities
• Information trade-offs for optical quantum communication
• Concavity of entropy under thinning
• The multi-mode quantum Entropy Power Inequality

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• The conditional Entropy Power Inequality for bosonic quantum systems
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• Gaussian optimizers for entropic inequalities in quantum information
• Approximate reversal of quantum Gaussian dynamics
• Capacities of Quantum Amplifier Channels
• The conditional entropy power inequality for quantum additive noise channels
• Bosonic quantum communication across arbitrarily high loss channels
• Geometric inequalities from phase space translations
• The Wehrl entropy has Gaussian optimizers
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Norms of quantum Gaussian multi-mode channels
• 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
• On the minimum output entropy of single-mode phase-insensitive Gaussian channels
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Computable limits of optical multiple-access communications
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels
• Stabilizing Preparation of Quantum Gaussian States via Continuous Measurement