  Suppose that a system is known to be in one of two quantum states, $|\psi_1 >
$ or $|\psi_2 >$. If these states are not orthogonal, then in conventional
quantum mechanics it is impossible with one measurement to determine with
certainty which state the system is in. However, because a non-Hermitian
PT-symmetric Hamiltonian determines the inner product that is appropriate for
the Hilbert space of physical states, it is always possible to choose this
inner product so that the two states $|\psi_1 > $ and $|\psi_2 > $ are
orthogonal. Thus, quantum state discrimination can, in principle, be achieved
with a single measurement.
