  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.
