PT-symmetric quantum state discrimination

Suppose that a system is known to be in one of two quantum states. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of determining with one measurement 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 are orthogonal. Thus, it is possible to perform a simulated quantum state discrimination with a single measurement in which a perfect state discrimination is realized probabilistically.