Abstract
Some quantum measurements cannot 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 latter with quantum state discrimination.
- Received 8 January 2019
- Corrected 16 April 2019
DOI:https://doi.org/10.1103/PhysRevLett.122.130403
© 2019 American Physical Society
Physics Subject Headings (PhySH)
Corrections
16 April 2019
Correction: Missing information in Refs. [15–17] has been inserted.