On a conjecture regarding quantum hypothesis testing

Abstract: In this MSc thesis I consider the asymptotic behaviour of the symmetric error in composite hypothesis testing. In the classical case, when the null and alternative hypothesis are finite sets of states, the best achievable symmetric error exponent is simply the the best achievable symmetric error exponent corresponding to the "worst case pair". The conjecture -- raised several years ago -- is that this remains true in the quantum case, too. This is known to be true in some special case. However, all of the known special cases are in some sense "too nice", e.g., have certain symmetries. Hoping to find a counter-example, in my thesis I consider a new special case, which on one hand is as "asymmetrical" as possible, yet still analytically computable. However, as it turns out from some involved computation, the conjecture is also true in this case, and thus gives further evidence to this conjecture.