Violating the Modified Helstrom Bound with Nonprojective Measurements

TL;DR

This paper demonstrates that nonprojective quantum measurements can surpass the modified Helstrom bound in state discrimination tasks, especially under certain cost functions, highlighting potential experimental advantages.

Contribution

It introduces a new framework showing nonprojective measurements outperform projective ones in quantum state discrimination with tunable costs, including robustness to noise.

Findings

Nonprojective measurements can outperform projective measurements for specific cost functions.

The modified Helstrom bound is rigorously derived for projective measurements.

Certain nonprojective measurement strategies are robust against experimental noise.

Abstract

We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a non-guess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and non-guess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case. We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement. Notably, while the cost advantage of the latter protocol is destroyed with the introduction of any amount of experimental noise, other choices of cost function have optima for which nonprojective measurements robustly show an appreciable, and thus experimentally measurable, cost advantage. Such an experiment would be an unambiguous demonstration of a benefit from nonprojective measurements.