TY - JOUR
T1 - All sets of incompatible measurements give an advantage in quantum state discrimination
AU - Skrzypczyk, Paul
AU - Supic, Ivan
AU - Cavalcanti, Daniel
PY - 2019/4/2
Y1 - 2019/4/2
N2 - 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.
AB - 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.
KW - quantum measurements
KW - quantum nonlocality
KW - resource theories
UR - http://www.scopus.com/inward/record.url?scp=85064040805&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.122.130403
DO - 10.1103/PhysRevLett.122.130403
M3 - Article
VL - 122
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 13
M1 - 130403
ER -