TY - JOUR
T1 - Quantifying measurement incompatibility of mutually unbiased bases
AU - Designolle, Sebastien
AU - Skrzypczyk, Paul
AU - Frowis, Florian
AU - Brunner, Nicolas
PY - 2019/2/8
Y1 - 2019/2/8
N2 - Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d+ 1 MUB (given d is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.
AB - Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k = d+ 1 MUB (given d is a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.
UR - https://arxiv.org/abs/1805.09609
U2 - 10.1103/PhysRevLett.122.050402
DO - 10.1103/PhysRevLett.122.050402
M3 - Article
VL - 122
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
M1 - 050402
ER -