2018/05/31 by Sébastien Designolle, Paul Skrzypczyk, Florian Fröwis +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Dimension (graph theory) #Discrete mathematics #Mathematical analysis #Mathematics #Mutually unbiased bases #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Robustness (evolution) #Statistical physics #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1103/physrevlett.122.050402
published as Phys. Rev. Lett. 122, 050402 (2019) · 12 pages
openalex publication_date 2019/02/06 · arxiv created 2020/04/17 · arxiv updated 2020/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 (using the standard construction for d being 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.