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Preserver Problems on Quantum Structures
Speaker Speaker: Prof. Lajos Molnar (University of Debrecen)
Data Evento Lunedì 17 Dicembre 2012, alle ore 16:30 - Aula dei seminari
The typical general preserver problem reads as follows. Given a structure X,
determine all transformations on X which preserve

-a given operation among the elements of X, or
-a given relation among the elements of X, or
-a quantity attached to the elements of X,
etc.
Preserver transformations can be viewed as morphisms
or symmetries of the underlying structure X. For example, Wigner's famous
theorem on the structure of quantum mechanical symmetry transformations
can also be regarded as the solution of a particular preserver problem.

In this talk we first give several examples of such problems that appear in different areas
of mathematics. In the second part we present some of our results concerning
preserver transformations on certain quantum structures.

We consider transformations on the spaces of density operators (quantum states),
self-adjoint operators (observables), Hilbert spaces effects which preserve
quantum relative entropy, order, commutativity (comparability), the operation
of sequential product, etc.