Mixed discrete variable Gaussian states

TL;DR

This paper introduces a finite-dimensional analogue of mixed Gaussian states in quantum systems, filling a gap in the mathematical framework for discrete variable quantum states.

Contribution

It proposes a new definition for mixed discrete Gaussian states based on formulas from pure discrete Gaussian states, extending the theoretical understanding.

Findings

Defined mixed discrete Gaussian states mathematically

Provided explicit formulas for these states

Bridged the gap between pure and mixed discrete Gaussian states

Abstract

The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual infinite-dimensional case. There exist finite versions for most of the elements used in the continuous case, but (to our knowledge) there does not exist a finite version corresponding to the mixed Gaussian states. Our aim is to fill this gap. The definition we propose for the mixed discrete Gaussian states is based on the explicit formulas we have obtained in the case of pure discrete variable Gaussian states.