All $d\otimes d$ dimensional entangled states are useful for the antidiscrimination of quantum measurements when $d$ is even

TL;DR

This paper demonstrates that all entangled states in even-dimensional systems are useful for the task of quantum measurement antidiscrimination, extending the understanding of entanglement's role in quantum channel tasks.

Contribution

It shows that for every even-dimensional entangled state, there exist sets of measurements that are antidiscriminable with that state but not with product states, highlighting the usefulness of entanglement in this context.

Findings

All even-dimensional entangled states enable antidiscrimination of certain measurement sets.

Product states cannot achieve the same antidiscrimination capability.

The result extends the utility of entanglement beyond channel discrimination to measurement antidiscrimination.

Abstract

Piani and Watrous [Phys. Rev. Lett.102, 250501 (2009)] proved that all entangled states are useful for discrimination of quantum channels. We pose the same question in the context of antidiscrimination of quantum channels. We partially answer this by showing that for every $d\otimes d$ entangled state (with even $d$), there exist three projective measurements which are antidiscriminable (but not discriminable) with that input state but those three measurements are not antidiscriminable with the product probe.