Feynman's path integral and mutually unbiased bases

TL;DR

This paper explores the connection between Feynman's path integral and mutually unbiased bases in finite-dimensional quantum systems, providing new insights into the underlying structure of quantum propagators.

Contribution

It demonstrates that the property of mutual unbiasedness of temporally proximal bases underpins Feynman's path integral, supported by a finite-dimensional approximation of quantum mechanics.

Findings

Confirmed mutual unbiasedness of short-time propagators

Established finite-dimensional analogue of free quantum particle

Linked path integral properties to basis mutual unbiasedness

Abstract

Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may lie in the property of mutual unbiasedness of temporally proximal bases. We confirm the corresponding property of the short-time propagator by using a specially devised N x N -approximation of quantum mechanics in L^2(R) applied to our finite-dimensional analogue of a free quantum particle.