Another look at the optimal Bayes cost in the binary decision problem

TL;DR

This paper explores a novel quantum state discrimination strategy involving isoenergetic compression of a potential well, demonstrating that the Helstrom bound can sometimes be surpassed for lower error probabilities.

Contribution

It introduces a new approach to quantum state discrimination by modifying the potential well, potentially achieving error rates below the Helstrom bound.

Findings

Helstrom bound can be violated with the new strategy

Modified wave-functions improve discrimination accuracy

Isoenergetic compression affects quantum measurement outcomes

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 for the state discrimination is known to be given by the Helstrom bound. A new strategy is introduced here whereby the square well is compressed isoenergetically, modifying the wave-functions. The new contracted chamber is then probed using the conventional optimal strategy, and the error probability is calculated. It is shown that in some cases the Helstrom bound can be violated, i.e. the state discrimination can be realized with a smaller error probability.