A. Szymusiak (JU): Morphophoric quantum measurements, generalised qplexes, and 2-designs
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-04-23

Anna Szymusiak (Jagiellonian University)
Morphophoric quantum measurements, generalised qplexes, and 2-designs.
We study the class of generalised quantum measurements (POVMs) with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to this set and call such measurements morphophoric. This leads to the generalisation of the notion of a qplex, where SIC-POVMs are replaced by the elements of the much larger class of morphophoric POVMs, containing in particular 2-design (rank-1 and equal-trace) POVMs. The intrinsic geometry of a generalised qplex is the same as that of the set of quantum states, so we explore its external geometry, investigating, inter alia, the algebraic and geometric form of the inner (basis) and the outer (primal) polytopes between which the generalised qplex is sandwiched. In particular, we examine generalised qplexes generated by MUB-like 2-design POVMs utilizing their graph-theoretical properties.
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