Enhanced quantum state discrimination under general measurements with entanglement and nonorthogonality restrictions

TL;DR

This paper investigates how quantum state discrimination can surpass the Helstrom limit by employing non-positive measurements, even without initial entanglement, thus broadening the understanding of quantum measurement strategies.

Contribution

It demonstrates that non-positive measurements can be realized without initial entanglement, enabling improved quantum state discrimination beyond traditional bounds.

Findings

Sub-Helstrom error probabilities achieved with non-positive measurements.

Initial product states can produce effective non-positive measurements.

Entanglement is not necessary for surpassing Helstrom limit.

Abstract

The minimum error probability for distinguishing between two quantum states is bounded by the Helstrom limit, derived under the assumption that measurement strategies are restricted to positive operator-valued measurements. We explore scenarios in which the error probability for discriminating two quantum states can be reduced below the Helstrom bound under some constrained access of resources, indicating the use of measurement operations that go beyond the standard positive operator-valued measurements framework. We refer to such measurements as non-positive operator-valued measurements. While existing literature often associates these measurements with initial entanglement between the system and an auxiliary, followed by joint projective measurement and discarding the auxiliary, we demonstrate that initial entanglement between system and auxiliary is not necessary for the emergence of such measurements in the context of state discrimination. Interestingly, even initial product states can give rise to effective non-positive measurements on the subsystem, and achieve sub-Helstrom discrimination error when discriminating quantum states of the subsystem.