On 1-qubit channels

Abstract

The entropy H_T(rho) of a state rho with respect to a channel T and the Holevo capacity of the channel require the solution of difficult variational problems. For a class of 1-qubit channels, which contains all the extremal ones, the problem can be significantly simplified by associating an Hermitian antilinear operator theta to every channel of the considered class. The concurrence of the channel can be expressed by theta and turns out to be a flat roof. This allows to write down an explicit expression for H_T. Its maximum would give the Holevo (1-shot) capacity.

12 pages, several printing or latex errors corrected

References in corpus (4)

• Entanglement Measures under Symmetry
• The Entanglement of Formation for Isotropic States
• Minimal Entropy of States Emerging from Noisy Quantum Channels
• A Characterization of Completely-Positive Trace-Preserving Maps on 2x2 Matrices

Cited by in corpus (5)

• Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry
• On quantum channels
• Qubit channels that achieve capacity with two states
• Efficient accessible bounds to the classical capacity of quantum channels
• Experimental Lower Bounds to the Classical Capacity of Quantum Channels