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

TL;DR

This paper develops alternative, information-theoretic uncertainty relations within the decoherent histories framework of quantum mechanics, providing improved bounds on probabilities and Shannon information in various physical scenarios.

Contribution

It introduces new formulations of uncertainty relations using Shannon information and develops methods to better estimate probabilities in decoherent histories.

Findings

Improved upper bounds for the probability of projection histories.

Enhanced lower bounds for Shannon information.

Application of results to physically relevant quantum systems.

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.