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The problem of quantum state discrimination between two wave functions of aparticle in a square well potential is considered. The optimal minimum-errorprobability is known to be given by the Helstrom bound. A new strategy isintroduced by inserting an impenetrable barrier in the middle of the squarewell, which is either a nodal or non-nodal point of the wave function. Theenergy required to insert the barrier is dependent on the initial state. Thisenables the experimenter to gain additional information beyond the standardprobing of the state envisaged by Helstrom and to improve thedistinguishability of the states. It is shown that under some conditions theHelstrom bound can be violated, i.e. the state discrimination can be realizedwith a smaller error probability.

Reexamination of the optimal Bayes cost in the binary decision problem