One-mode Bosonic Gaussian channels: a full weak-degradability classification

Abstract

A complete degradability analysis of one-mode Gaussian Bosonic channels is presented. We show that apart from the class of channels which are unitarily equivalent to the channels with additive classical noise, these maps can be characterized in terms of weak- and/or anti-degradability. Furthermore a new set of channels which have null quantum capacity is identified. This is done by exploiting the composition rules of one-mode Gaussian maps and the fact that anti-degradable channels can not be used to transfer quantum information.

23 pages, 3 figures

References in corpus (18)

• Quantum information with continuous variables
• The capacity of the noisy quantum channel
• Optimal Quantum Cloning Machines
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Information transmission through a noisy quantum channel
• Classical capacity of the lossy bosonic channel: the exact solution
• Information-capacity description of spin-chain correlations
• Minimum output entropy of bosonic channels: a conjecture
• Strong and Electromagnetic Decays of Two New $Lambd{a}_c^{\ast }$ Baryons
• Entanglement assisted capacity of the broadband lossy channel
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Additivity properties of a Gaussian Channel
• Broadband channel capacities
• Minimum Renyi and Wehrl entropies at the output of bosonic channels
• The Holevo capacity of infinite dimensional channels and the additivity problem
• On Shor's channel extension and constrained channels
• Effective field theory and fundamental interactions

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