Reexamination of the optimal Bayes cost in the binary decision problem

TL;DR

This paper proposes a novel method involving barrier insertion in a quantum well to improve state discrimination, potentially surpassing the traditional Helstrom bound by gaining extra information through energy-dependent barrier insertion.

Contribution

It introduces a new strategy for quantum state discrimination that can violate the Helstrom bound by using energy-dependent barrier insertion in a square well.

Findings

Helstrom bound can be violated under certain conditions

Barrier insertion provides additional information for state discrimination

Improved distinguishability of quantum states beyond standard methods

Abstract

The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting an impenetrable barrier in the middle of the square well, which is either a nodal or non-nodal point of the wave function. The energy required to insert the barrier is dependent on the initial state. This enables the experimenter to gain additional information beyond the standard probing of the state envisaged by Helstrom and to improve the distinguishability of the states. It is shown that under some conditions the Helstrom bound can be violated, i.e. the state discrimination can be realized with a smaller error probability.