Capacities of the covariant Pauli channel

Abstract

We study the four well-known capacities of a two-parameter family of qubit Pauli channels. These are the channels which are covariant under the SO(2) group and contain the depolarizing channel as a special case. We find exact expressions for the classical capacity and entanglement assisted capacities, and analytically determine the regions where the quantum capacity of the channel vanishes. We then use a flag extension to find upper bound for the quantum capacity and private capacity of these channels in the entire region of parameter space and also obtain the lower bound for the quantum capacity by calculating the single shot quantum capacity numerically. In conjunction with previous results on depolarizing channels, our result is one step forward for determining the capacities of the full Pauli channel.

arXiv commentReferences added, Accepted for publication in Physical Review A

References in corpus (33)

• Separability Criterion for Density Matrices
• The capacity of the noisy quantum channel
• General Entanglement Breaking Channels
• Superadditivity of communication capacity using entangled inputs
• A Survey on Quantum Channel Capacities
• Additivity for a class of unital qubit channels
• Counterexample to an additivity conjecture for output purity of quantum channels
• The structure of degradable quantum channels
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• On some additivity problems in quantum information theory
• The private capacity of quantum channels is not additive
• The quantum capacity with symmetric side channels
• Continuity of quantum channel capacities
• Approximate Degradable Quantum Channels
• Simplifying additivity problems using direct sum constructions
• Comments on Hastings' Additivity Counterexamples
• Quantum entanglement and classical communication through a depolarising channel
• Quantum and private capacities of low-noise channels
• Classical and quantum capacities of a fully correlated amplitude damping channel
• Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0
• Quantum flags, and new bounds on the quantum capacity of the depolarizing channel
• Quantum capacity analysis of multi-level amplitude damping channels
• Quantum capacity of bosonic dephasing channel
• Selfcomplementary quantum channels
• Estimating Quantum and Private capacities of Gaussian channels via degradable extensions
• Extending additivity from symmetric to asymmetric channels
• The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension
• Simplification of additivity conjecture in quantum information theory
• Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity
• Detecting Incapacity
• Capacities of Gaussian Quantum Channels with Passive Environment Assistance
• Quantum informational properties of the Landau-Streater channel
• A Characterization of Antidegradable Qubit Channels

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