1204.5107 (A. Vourdas)

Partial order and divisor topology in a set of finite quantum systems    [PDF]

A. Vourdas

A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states, density matrices, etc) into their counterparts in the supersystem $\Sigma (n)$ (for $m|n$). The compatibility of these embeddings is studied. The concept of ubiquity is introduced for quantities which fit with this structure. It is shown that various entropic quantities are ubiquitous, but various phase space quantities (e.g., Wigner and Weyl functions) are nonubiquitous. The sets of various quantities become topological spaces with the divisor topology, which encapsulates fundamental physical properties. The continuity of various maps among these sets is studied.

View original: http://arxiv.org/abs/1204.5107