Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results

Abstract

A formulation of the generalized minimal output entropy conjecture for Gaussian channels is presented. It asserts that, for states with fixed input entropy, the minimal value of the output entropy of the channel (i.e. the minimal output entropy increment for fixed input entropy) is achieved by Gaussian states. In the case of centered channels (i.e. channels which do not add squeezing to the input state) this implies that the minimum is obtained by thermal (Gibbs) inputs. The conjecture is proved to be valid in some special cases.

7 pages, updated version minor typos corrected

References in corpus (5)

• Superadditivity of communication capacity using entangled inputs
• Quantum Capacities of Bosonic Channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Degradability of Bosonic Gaussian channels
• Multi-mode bosonic Gaussian channels

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• A Survey on Quantum Channel Capacities
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Quantum channels and their entropic characteristics
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• A solution of the Gaussian optimizer conjecture
• Quantum state majorization at the output of bosonic Gaussian channels
• The entropy power inequality for quantum systems
• Quantum trade-off coding for bosonic communication
• Limits on classical communication from quantum entropy power inequalities
• Fundamental limits on quantum dynamics based on entropy change
• Information trade-offs for optical quantum communication
• Renyi relative entropies of quantum Gaussian states
• Gaussian optimizers for entropic inequalities in quantum information
• Electromagnetic channel capacity for practical purposes
• Minimum output entropy of a non-Gaussian quantum channel
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Thermal equilibrium in Gaussian dynamical semigroups
• Classical capacity of phase-sensitive Gaussian quantum channels
• A de Bruijn identity for discrete random variables
• The free space optical interference channel
• Fluctuation and dissipation in memoryless open quantum evolutions
• A Meta Logarithmic-Sobolev Inequality for Phase-Covariant Gaussian Channels