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

Understand

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.