Measures of Distance in Quantum Mechanics

Author:

Gusin Pawel1ORCID,Burys Daniel1ORCID,Radosz Andrzej1

Affiliation:

1. Department of Quantum Technologies, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland

Abstract

Combining gravity with quantum theory is still a work in progress. On the one hand, classical gravity is the geometry of space-time determined by the energy–momentum tensor of matter and the resulting nonlinear equations; on the other hand, the mathematical description of a quantum system is Hilbert space with linear equations describing evolution. In this paper, various measures in Hilbert space will be presented. In general, distance measures in Hilbert space can be divided into measures determined by energy and measures determined by entropy. Entropy measures determine quasi-distance because they do not satisfy all the axioms defining distance. Finding a general rule to determine such a measure unambiguously seems to be fundamental.

Publisher

MDPI AG

Subject

General Physics and Astronomy

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