Open AccessCovariant stochastic products of quantum states
Author(s) -
Paolo Aniello
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1416/1/012002
Subject(s) - mathematics , pure mathematics , covariant transformation , nuclear operator , trace class , hilbert space , operator algebra , abelian group , subalgebra , compact quantum group , group (periodic table) , compact group , convex set , algebra over a field , finite rank operator , banach space , group algebra , regular polygon , lie group , quantum mechanics , convex optimization , physics , geometry
A notion of stochastic product of quantum states — a binary operation on the set of density operators preserving the convex structure — is discussed. We describe, in particular, a class of group-covariant, associative stochastic products: the twirled products . Each binary operation in this class can be constructed by means of a square integrable projective representation of a locally compact group, a probability measure on this group and a fiducial density operator in the Hilbert space of the representation. By suitably extending this operation from the convex set of density operators to the full Banach space of trace class operators, one obtains a Banach algebra, which is commutative in the case where the relevant group is abelian.