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We investigate how to define in a consistent way the probabilities of thetransitions between the "flavor" states of the two-level quantum system, whichis described by a non-Hermitian but parity and time-reversal (PT) symmetricHamiltonian. Explicit calculations are carried out to demonstrate theconservation of probability if a proper definition of the final state isadopted. Finally, this formalism is applied to two-flavor neutrino oscillations$\nu^{}_\mu \to \nu^{}_\mu$ and $\nu^{}_\mu \to \nu^{}_\tau$ in vacuum, wherethe exact PT symmetry requires the vacuum mixing angle to be maximal, which iscompatible with current neutrino oscillation experiments. A possiblegeneralization to the three-flavor case is briefly discussed.

Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians