The Helstrom measurement: A nondestructive implementation

TL;DR

This paper presents a new method to implement Helstrom's minimum error measurement nondestructively by entangling the system with an ancilla, enabling optimal discrimination in cases where direct measurement is challenging.

Contribution

It introduces an entanglement-based, nondestructive implementation of Helstrom measurement that is feasible for complex states and preserves the system for further processing.

Findings

Achieves Helstrom bound through entanglement transformation

Provides a feasible alternative for continuous variable states

Enables non-destructive measurement with post-measurement state control

Abstract

We discuss a novel implementation of the minimum error state discrimination measurement, originally introduced by Helstrom. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first entangled to an ancillary system and the measurement is performed on the ancilla. We show that, by an appropriate choice of the entanglement transformation, the Helstrom bound can be attained. The advantage of this approach is twofold. First, it provides a novel implementation when the optimal projective measurement cannot be directly performed. For example, in the case of continuous variable states (binary and N phase-shifted coherent signals), the available detection methods, photon counting and homodyning, are insufficient to perform the required cat-state projection. In the case of symmetric states, the square-root measurement is optimal, but it is not easy to perform directly for more than two states. Our approach provides a feasible alternative in both cases. Second, the measurement is non-destructive from the point of view of the original system and one has a certain amount of freedom in designing the post-measurement state, which can then be processed further.