Sharpened Information-Theoretic Uncertainty Relations and the Histories Approach to Quantum Mechanics

Abstract

In this paper alternative formulations of the conventional uncertainty relation are studied in the context of decoherent histories. The results are given in terms of Shannon information. A variety of methods are developed to evaluate the upper bound for the probability of two or more projection histories. The methods employed give improved limits for the maximal achievable probability and an improved lower bound for the Shannon information. The results are then applied to a number of physically relevant situations.