The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers

Abstract

We determine the p->q norms of the Gaussian one-mode quantum-limited attenuator and amplifier and prove that they are achieved by Gaussian states, extending to noncommutative probability the seminal theorem "Gaussian kernels have only Gaussian maximizers" (Lieb in Invent Math 102(1):179-208, 1990). The quantum-limited attenuator and amplifier are the building blocks of quantum Gaussian channels, which play a key role in quantum communication theory since they model in the quantum regime the attenuation and the noise affecting any electromagnetic signal. Our result is crucial to prove the longstanding conjecture stating that Gaussian input states minimize the output entropy of one-mode phase-covariant quantum Gaussian channels for fixed input entropy. Our proof technique is based on a new noncommutative logarithmic Sobolev inequality, and it can be used to determine the p->q norms of any quantum semigroup.

Annales Henri Poincaré (2018)

References in corpus (12)

• 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
• Gaussian states minimize the output entropy of one-mode quantum Gaussian channels
• Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator
• Gaussian optimizers for entropic inequalities in quantum information
• Capacities of Quantum Amplifier Channels
• Norms of quantum Gaussian multi-mode channels
• Gaussian optimizers and other topics in quantum information
• On the minimum output entropy of single-mode phase-insensitive Gaussian channels
• Classical Information Capacity of the Bosonic Broadcast Channel
• The multi-mode quantum Entropy Power Inequality

Cited by in corpus (12)

• The conditional Entropy Power Inequality for bosonic quantum systems
• Gaussian optimizers for entropic inequalities in quantum information
• Approximate reversal of quantum Gaussian dynamics
• The conditional entropy power inequality for quantum additive noise channels
• 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
• Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
• On quantum Gaussian optimizers conjecture in the case q=p
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels