All sets of incompatible measurements give an advantage in quantum state discrimination

Abstract

Some quantum measurements can not be performed simultaneously, i.e. they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task. This is proven by showing that the Robustness of Incompatibility, a quantifier of how much noise a set of measurements tolerates before becoming compatible, has an operational interpretation as the advantage in an optimally chosen discrimination task. We also show that if we take a resource-theory perspective of measurement incompatibility, then the guessing probability in discrimination tasks of this type forms a complete set of monotones that completely characterize the partial order in the resource theory. Finally, we make use of previously known relations between measurement incompatibility and Einstein-Podolsky-Rosen steering to also relate the later with quantum state discrimination.

10 pages, no figures

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Joint measurability of generalized measurements implies classicality
• All entangled states are useful for channel discrimination
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Cited by in corpus (3)

• Operational relevance of resource theories of quantum measurements
• Multi-object operational tasks for convex quantum resource theories
• Incompatibility probability of random quantum measurements