Usefulness of $d\otimes d$ dimensional pure entangled states for antidiscrimination of quantum measurements when $d$ is even

Abstract

The usefulness of entanglement in quantum channel discrimination is a central topic in quantum information theory. A landmark result in this direction was established by Piani and Watrous [$Phys.Rev.Lett.102,250501(2009)$] who 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 pure entangled state of $\mathbbm{C}^d\otimes\mathbbm{C}^d$ (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.