J. Czartowski (JU): Mixed-State Designs and Isoentangled Mutually Unbiased Bases
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-04-15

Jakub Czartowski (Jagiellonian University).
Mixed-State Designs and Isoentangled Mutually Unbiased Bases.
Several optimal measurement schemes are closely related to discrete structures in Hilbert space We derive a complete set of five isoentangled mutually unbiased bases exists in dimension four by an explicit analytical construction [1]. Reduced density matrices of these 20 pure states form a regular dodecahedron inscribed in a sphere of radius sqrt(3/20) located inside the Bloch ball of radius 1/2. It provides an example of a mixed-state 2-design — a discrete set of quantum states such that the mean value of any quadratic function of density matrices is equal to the average over the entire set of mixed states with respect to the flat Hilbert-Schmidt measure. We establish necessary and sufficient conditions mixed-state designs need to satisfy and present general methods to construct them. We show that partial traces of a projective design in a composite Hilbert space form a mixed-state design, while decoherence of elements of a projective design yields a design in the classical probability simplex.
[1] J.Cz., D. Goyeneche, M. Grassl and K. Życzkowski, "Isoentangled Mutually Unbiased Bases, Symmetric Quantum Measurements, and Mixed-State Designs", PRL 2020, in press. 
CTP Quantum Information Days (online), 22-24 February 2021.
Center for Theoretical Physics PAS (Warsaw, Poland)