The structure of degradable quantum channels

By Toby S. Cubitt, Mary Beth Ruskai, Graeme Smith. 2008

146 citations recorded by the source corpus.

Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable, and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions (dB and dE, respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with an environment that is “small” in the sense of ΦC. Suc...

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/977384b1596ba0ec4b0cae9a2093a98fbaa2d18e