Generalized Contexts for Quantum Histories

Marcelo Losada, Roberto Laura

Marcelo Losada, Leonardo Vanni, Roberto Laura

Oliver Rudolph

A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of ‘‘history’’ is generalized to the notion of ‘‘effect history.’’ The space of effect histories carries the structure of a D-poset. Recent results of J. D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnès’ logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.

Adrian Kent

D. Sokolovski, Y. Liu

Satoshi Uchiyama

The functional composition principle is generalized by taking into account of history of context change. Analysis of Peres’ example shows hysteresis of value assignments. It is shown that value assignments depending on the history of context change are possible in the case that the Hilbert space of state vectors is finite dimensional.