Passive states optimize the output of bosonic Gaussian quantum channels

Abstract

An ordering between the quantum states emerging from a single mode gauge-covariant bosonic Gaussian channel is proven. Specifically, we show that within the set of input density matrices with the same given spectrum, the element passive with respect to the Fock basis (i.e. diagonal with decreasing eigenvalues) produces an output which majorizes all the other outputs emerging from the same set. When applied to pure input states, our finding includes as a special case the result of A. Mari, et al., Nat. Comm. 5, 3826 (2014) which implies that the output associated to the vacuum majorizes the others.

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• Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
• Capacities of Quantum Amplifier Channels
• The conditional entropy power inequality for quantum additive noise channels
• Geometric inequalities from phase space translations
• Quantum Zeno effect for open quantum systems
• The Wehrl entropy has Gaussian optimizers
• From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite Dimensions
• Continuous majorization in quantum phase space
• Passive states as optimal inputs for single-jump lossy quantum channels
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Spin squeezed GKP codes for quantum error correction in atomic ensembles
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• The Entropy Power Inequality with quantum conditioning
• Thinning, photonic beamsplitting, and a general discrete entropy power inequality
• Energy upper bound for structurally stable N-passive states
• Thermal equilibrium in Gaussian dynamical semigroups
• Majorization preservation of Gaussian bosonic channels
• On the minimum output entropy of single-mode phase-insensitive Gaussian channels
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• Fock majorization in bosonic quantum channels with a passive environment
• On discontinuity of information characteristics of quantum systems and channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Majorization ladder in bosonic Gaussian channels
• Fluctuation and dissipation in memoryless open quantum evolutions
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels