Discrete coherent and squeezed states of many-qudit systems

TL;DR

This paper develops a phase space framework for many-qudit systems using finite fields, introducing discrete coherent and squeezed states with properties similar to continuous systems, and explores their entanglement relations.

Contribution

It introduces a finite phase space approach for many-qudit systems, defining discrete coherent and squeezed states with novel properties and entanglement connections.

Findings

Defined discrete quasidistribution functions analogous to continuous ones.

Constructed finite coherent states based on a fiducial eigenstate.

Extended the framework to include discrete squeezed states and their entanglement relations.

Abstract

We consider the phase space for a system of $n$ identical qudits (each one of dimension $d$, with $d$ a primer number) as a grid of $d^{n} \times d^{n}$ points and use the finite field $GF(d^{n})$ to label the corresponding axes. The associated displacement operators permit to define $s$-parametrized quasidistribution functions in this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states between different qudits.