Abstract

Channel discrimination is in its simplest form is the hypothesis testing problem where we are given a black-box channel which can be one of two candidate channels and the task is to find out which one it is. We are interested in optimal asymptotic error rates for this problem, and in particular whether adaptivity (i.e. choosing the inputs of the channel uses based on previous outcomes) is required for optimal strategies. For the simple discrimination problem just described, it has previously been shown that adaptivity is asymptotically not required when the channels are classical, whereas in the quantum case adaptivity gives an advantage for the symmetric but not the asymmetric error exponent. We study the more general composite problem, i.e. the problem where we don’t have two single candidate channels, but two sets of candidate channels, and focus on the asymmetric case. There we show that for classical channels adaptivity can give an asymptotic advantage, however we also prove optimality of non-adaptive strategies when the sets of channels are convex. For the equivalent problem with quantum channels we prove an entropic expression for the Stein exponent using non-adaptive strategies.

The talk will start by introducing the problem for classical channels, and illustrate previous work and associated results. It will subsequently give a brief introduction of the required concepts from quantum information theory before addressing the quantum problem.