A solution of the Gaussian optimizer conjecture

Abstract

The long-standing conjectures of the optimality of Gaussian inputs for Gaussian channel and Gaussian additivity are solved for a broad class of covariant or contravariant Bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and amplifier channels) restricting to the class of states with finite second moments. We show that the vacuum is the input state which minimizes the entropy at the output of such channels. This allows us to show also that the classical capacity of these channels (under the input energy constraint) is additive and is achieved by Gaussian encodings.

24 pages, no figures (minor typos corrected)

References in corpus (4)

• Quantum channels and their entropic characteristics
• Quantum state majorization at the output of bosonic Gaussian channels
• Limits on classical communication from quantum entropy power inequalities
• The classical capacity of quantum thermal noise channels to within 1.45 bits

Cited by in corpus (64)

• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Simulating boson sampling in lossy architectures
• Quantum state majorization at the output of bosonic Gaussian channels
• The minimum error probability of quantum illumination
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Energy-constrained diamond norms and their use in quantum information theory
• Energy-constrained private and quantum capacities of quantum channels
• A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
• Entanglement cost and quantum channel simulation
• Enhanced noise resilience of the surface-GKP code via designed bias
• Majorization and additivity for multimode bosonic Gaussian channels
• Gaussian optimizers and the additivity problem in quantum information theory
• Passive states optimize the output of bosonic Gaussian quantum channels
• Gaussian Thermal Operations and the Limits of Algorithmic Cooling
• Gaussian states minimize the output entropy of one-mode quantum Gaussian channels
• Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model
• Coherent-state discrimination via non-heralded probabilistic amplification
• Normal form decomposition for Gaussian-to-Gaussian superoperators
• Gaussian optimizers for entropic inequalities in quantum information
• Multi-Phase Hadamard receivers for classical communication on lossy bosonic channels
• Quantum Energy Lines and the optimal output ergotropy problem
• Quantum-Classical Hybrid Systems and their Quasifree Transformations
• Approximate reversal of quantum Gaussian dynamics
• Convergence rates for the quantum central limit theorem
• Capacities of Quantum Amplifier Channels
• Restoring quantum communication efficiency over high loss optical fibres
• Relativistic quantum communication between harmonic oscillator detectors
• The conditional entropy power inequality for quantum additive noise channels
• The capacity of coherent-state adaptive decoders with interferometry and single-mode detectors
• Bosonic quantum communication across arbitrarily high loss channels
• Local optimization on pure Gaussian state manifolds
• Error mitigation on a near-term quantum photonic device
• Gaussian maximizers for quantum Gaussian observables and ensembles
• Strong converse rates for classical communication over thermal and additive noise bosonic channels
• Quantum-enabled communication without a phase reference
• On the constrained classical capacity of infinite-dimensional covariant quantum channels
• Quantum Channel Capacities Per Unit Cost
• Ultimate Capacity of a Linear Time-Invariant Bosonic Channel
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Quantum-optical channels that output only classical states
• Coherent information of one-mode Gaussian channels -- the general case of nonzero added classical noise
• Norms of quantum Gaussian multi-mode channels
• Quantum Optical Communication in the presence of strong attenuation noise
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• The information capacity of entanglement-assisted continuous variable measurement
• The Entropy Power Inequality with quantum conditioning
• Proof of the Gaussian maximizers conjecture for the communication capacity of noisy heterodyne measurements
• Uniform finite-dimensional approximation of basic capacities of energy-constrained channels
• Strong converse for the classical capacity of optical quantum communication channels
• The structure of general quantum Gaussian observable
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• Entanglement cost for infinite-dimensional physical systems
• Lower semicontinuity of the entropic disturbance and its applications in quantum information theory
• Making two particle detectors in flat spacetime communicate quantumly
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Quantum signal+noise models: beyond i.i.d
• The multi-mode quantum Entropy Power Inequality
• How cosmological expansion affects communication between distant quantum systems
• Computable limits of optical multiple-access communications
• Superior resilience of non-Gaussian entanglement against local Gaussian noises
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels
• Characterization of non-adaptive Clifford channels
• Classical capacity of quantum non-Gaussian attenuator and amplifier channels
• Quantum communication through a partially reflecting accelerating mirror