Informationentropy and the space of decoherence functions in generalised quantum theory
Abstract
In standard quantum theory, the ideas of informationentropy and of pure states are closely linked. States are represented by density matrices $\rho$ on a Hilbert space and the informationentropy $tr(\rho\log\rho)$ is minimised on pure states (pure states are the vertices of the boundary of the convex set of states). The space of decoherence functions in the consistent histories approach to generalised quantum theory is also a convex set. However, by showing that every decoherence function can be written as a convex combination of two other decoherence functions we demonstrate that there are no `pure' decoherence functions. The main content of the paper is a new notion of informationentropy in generalised quantum mechanics which is applicable in contexts in which there is no a priori notion of time. Informationentropy is defined first on consistent sets and then we show that it decreases upon refinement of the consistent set. This informationentropy suggests an intrinsic way of giving a consistent set selection criterion.
 Publication:

arXiv eprints
 Pub Date:
 December 1996
 DOI:
 10.48550/arXiv.quantph/9612035
 arXiv:
 arXiv:quantph/9612035
 Bibcode:
 1996quant.ph.12035I
 Keywords:

 Quantum Physics
 EPrint:
 31 pages, RevTeX