A squeezing formalism for finite dimensional quantum systems

TL;DR

This paper introduces a squeezing transformation for finite-dimensional quantum systems, extending the concept of squeezing from continuous variables to discrete systems, with implications for spin squeezing and quantum state reproduction.

Contribution

It develops a formalism for squeezing in finite-dimensional quantum systems, bridging continuous and discrete quantum variable concepts.

Findings

Defines a squeezing operator for finite vector spaces.

Connects the formalism to spin squeezing and quantum state reproduction.

Provides a mathematical framework for finite-dimensional squeezing.

Abstract

This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real line, that is, a transformation capable to diminish (or enhance) the mean square deviation of a centered distribution. As it is discussed, the definition of such an operator on finite dimensional vector spaces is not a trivial matter, but, on the other hand, has obvious connections with problems such as spin squeezing and (finite) quantum state reproduction.