Lecturer: Farkas Máté (KCIK, University of Gdansk)

Mutually unbiased bases (MUBs) play an important role in quantum information, as they provide optimal measurement bases for many protocols, and maximize certain uncertainty and incompatibility measures. Sets of MUBs can be classified into equivalence classes, using equivalence transformations -- that is, all possible operations that leave invariant the MUB conditions. The interpretation of these classes is mathematically clear, nevertheless, their physical meaning is vague. Recently (arXiv:1709.04898), it has been pointed out that different MUB n-tuples (with n>2) perform differently in the quantum random access codes (QRAC) protocol, in certain dimensions. Later, it was noted (arXiv:1706.04446) that these n-tuples are coming from different equivalence classes. In this talk, I will concentrate on pairs of MUBs (n=2). It turns out that even in this case, the MUB conditions are not enough to completely determine the behaviour of two measurement bases in certain tasks. For this to show, I will use a modified QRAC game, and propose new types of uncertainty relations. We will see that different equivalence classes of MUB pairs give different results in dimension 4, where a one-parameter family of equivalence classes of pairs exists.

This is a joint work with Jędrzej Kaniewski and Marcin Pawłowski.