The Topological Model for a Qubit: Quantum States in the Sheaf Framework

Antonina N. Fedorova and Michael G. Zeitlin

IPME RAS, St.Petersburg, Russia

http://www.ipme.ru/zeitlin.html

http://mp.ipme.ru/zeitlin.html,

anton@math.ipme.ru

zeitlin@math.ipme.ru


We consider some generalization of the theory of quantum states, which is based
on the analysis of long standing problems and unsatisfactory situation with
existing interpretations of quantum mechanics.
We demonstrate that the consideration of quantum states as sheaves can provide,
in principle, more deep understanding of some well-known phenomena.
The key ingredients of the proposed construction are the families of sections 
of sheaves with values in the proper category of the functional realizations of
infinite-dimensional Hilbert spaces with special (multiscale) filtrations
decomposed into the (entangled) orbits generated by actions/representations of
internal hidden symmetries.
In such a way, we open a possibility for the exact description of a lot of
phenomena like entanglement and measurement, wave function collapse,
self-interference, instantaneous quantum interaction, Multiverse, hidden 
variables, etc.
In the companion paper we consider the machinery needed for the generation of a
zoo of the complex quantum patterns during Wigner-Weyl-Moyal evolution together
with constructive algebraic control.