The Bayes cost in the binary decision problem

TL;DR

This paper explores a novel quantum state discrimination strategy involving barrier insertion, which can potentially reduce error probabilities below the Helstrom bound under ideal conditions.

Contribution

It introduces a new approach using barrier insertion to improve quantum state discrimination beyond traditional limits.

Findings

Barrier insertion creates nodes that aid in state distinction.

The method can violate the Helstrom bound under idealized conditions.

Modified wave functions enable lower error probabilities.

Abstract

The problem of quantum state discrimination between two wave functions on a ring is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting either adiabatically or instantaneously an impenetrable barrier. The insertion point, independent of the shape of the initial wave function, becomes a node. The resulting modified wave functions can be, if the initial functions are judiciously chosen, distinguished with a smaller error probability, and as a consequence the Helstrom bound can be violated under idealised conditions.