Gaussian states and geometrically uniform symmetry

TL;DR

This paper explores the properties of Gaussian quantum states under geometrically uniform symmetry, demonstrating how this symmetry simplifies optimal measurement derivations and applying it to multimode Gaussian states in quantum communication.

Contribution

It generalizes the application of geometrically uniform symmetry to multimode Gaussian states and analyzes its impact on optimal quantum measurements in communication systems.

Findings

Geometrically uniform symmetry applies to multimode Gaussian states.

Symmetry simplifies the derivation of optimal quantum measurements.

Application to pulse position modulation in quantum communication.

Abstract

Quantum Gaussian states can be considered as the majority of the practical quantum states used in quantum communications and more generally in quantum information. Here we consider their properties in relation with the geometrically uniform symmetry, a property of quantum states that greatly simplifies the derivation of the optimal decision by means of the square root measurements. In a general framework of the $N$-mode Gaussian states we show the general properties of this symmetry and the application of the optimal quantum measurements. An application example is presented, to quantum communication systems employing pulse position modulation. We prove that the geometrically uniform symmetry can be applied to the general class of multimode Gaussian states.