Iso-entangled Mutually Unbiased Bases and Mixed-state T-Designs
May 4th, 2021 KAROL ŻYCZKOWSKI Jagiellonian University

A Euclidean design is a finite set of points in Rn with certain approximation properties. This concept can be generalized to give the notion of pure-state designs: vectors selected in such a way that the average values of the first t moments averaged over the design coincide with the moment obtained by integrating over the set of all states. We introduce a related notion of a mixed-state t-design, which consist of a finite number of density matrices of order N with analogous properties. Mixed-state designs can be obtained by partial trace of pure states of size N2 forming a pure state design. We construct a set of five iso-entangled Mutually Unbiased Bases (MUBs) in H4, consisting of 20 pure states with the same degree of entanglement. Performing a partial trace on any of both subsystems leads to 20 single-qubit mixed states which form a regular dodecahedron inside the Bloch ball and a mixed 3-design.

Due to recommendations in place to contribute containing the spreading of COVID-19, the Theory Lectures will be carried out remotely via Zoom. In case you want to receive an invitation to attend the online session, you can send an email to Giovanna.Petrillo at

Tuesday, May 5, 2021, 10:00. Online (Zoom).