Additivity properties of a Gaussian Channel

Abstract

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Re'nyi entropies at the output of a channel. The conjecture is proven true for all Re'nyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment.

9 pages, 1 figure (minor error present in the published version corrected)

Cited by in corpus (31)

• Gaussian Quantum Information
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Minimum output entropy of bosonic channels: a conjecture
• Entropic Uncertainty Relations in Quantum Physics
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
• Quantum state majorization at the output of bosonic Gaussian channels
• Degradability of Bosonic Gaussian channels
• Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Bosonic Memory Channels
• Minimum Renyi and Wehrl entropies at the output of bosonic channels
• Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs
• Majorization and additivity for multimode bosonic Gaussian channels
• Gaussian optimizers and the additivity problem in quantum information theory
• Classical information capacity of a class of quantum channels
• Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results
• Nonadditivity effects in classical capacities of quantum multiple-access channels
• Electromagnetic channel capacity for practical purposes
• Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p
• Methods for Estimating Capacities and Rates of Gaussian Quantum Channels
• Qubit quantum channels: A characteristic function approach
• Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum
• Transition of D- Level Quantum Systems Through Quantum Channels with Correlated Noise
• A new approach to characterize qubit channels
• Non-commutative Rényi Entropic Uncertainty Principles
• Stasistically constrained operator associated with additivity of communication channel
• Multiplicativity properties of entrywise positive maps