Quantifying measurement incompatibility of mutually unbiased bases

Sebastien Designolle, Paul Skrzypczyk, Florian Frowis, Nicolas Brunner

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)
236 Downloads (Pure)


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.
Original languageEnglish
Article number050402
Number of pages6
JournalPhysical Review Letters
Issue number5
Early online date6 Feb 2019
Publication statusPublished - 8 Feb 2019

Structured keywords

  • Bristol Quantum Information Institute
  • QITG


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