SU(1,1) symmetry of multimode squeezed states

TL;DR

This paper demonstrates that certain multimode optical transformations involving linear optics and two-mode squeezing can be described by SU(1,1) operators, providing a new basis for analyzing non-Gaussian quantum states in continuous variable quantum information.

Contribution

It introduces an SU(1,1) framework for multimode optical transformations, extending analysis beyond Gaussian states and applicable to complex quantum optical networks.

Findings

New SU(1,1) basis for multimode transformations

Application to non-Gaussian quantum states

Extension to general quantum optical networks

Abstract

We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-the-art continuous variable quantum information experiments including quantum state sharing, quantum teleportation, and multipartite entangled states. Using this SU(1,1) description of these transformations, we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often-used restriction to Gaussian states. We analyze this basis, show its application to a class of transformations, and discuss its extension to more general quantum optical networks.