Complexity and capacity bounds for quantum channels

27/10/2017, 14:00 - 15:00 in MAP/0G/018

Rupert Levene, University College Dublin

Abstract:

We generalise some graph parameters to non-commutative graphs (a.k.a. operator systems of matrices) and quantum channels. In particular, we introduce the quantum complexity of a non-commutative graph, generalising the minimum semidefinite rank. These parameters give upper bounds on the Shannon zero-error capacity of a quantum channel which can beat the best general upper bound in the literature, namely the quantum Lovász theta number.