Operator Algebras and Identities

Chang Ho Choi, Joung Young Sug, Sang Don Choi +1 more

We prove that the relaxation functions in condensed matter physics can be easily calculated by the operator algebra technique in the continued fraction representation scheme. The Dyson equation for the single particle Green's function in the Hubbard model obtained in this way is identical with the one derived by Fedro and Willson in the lowest order approximation. And the cyclotron transition absorption formula obtained by this technique is identical with that of Argyres and Sigel.

Stanisław Goldstein, Andrzej Łuczak, Ivan F. Wilde

Jan Hamhalter

David W. Kribs, Jeremy Livick, Mike I. Nelson +2 more

We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private operator algebras, and operator spaces such as multiplicative domains and nullspaces of quantum channels and their complementary maps. For the case of privatizing to quantum states, we also derive dimension inequalities on the associated operator algebras that further quantify the trade-off between correction and privacy.

Robert G. Mortimer

Etang Chen

The axioms of measurements introduced by Ludwig are formulated and studied in the framework of operator algebras. It is shown that a concrete C*-algebra with identity satisfies the axiom of sensitivity increase of effects if and only if it is a von Neumann algebra; although a von Neumann algebra satisfies the axiom of decompossability of ensembles, however, the axiom of components of the mixtures of two ensembles is true only if a von Neumann algebra is a factor of type In (n < + ∞). It is also verified that the set of decision effects, which is proved to be a subset of projections of a von Neumann algebra, has similar lattice structure of quantum mechanics, and its connection with quantum logic in the sense of Varadarjan is also figured out.