Local complementation rule for continuous-variable four-mode unweighted graph states

TL;DR

This paper introduces local Gaussian transformations for continuous-variable four-mode unweighted graph states, advancing the understanding of their local equivalence classes and transformation rules.

Contribution

It derives the local Gaussian transformations corresponding to local complementation for four-mode CV graph states, expanding the framework beyond qubit Clifford unitaries.

Findings

Derived local Gaussian transformations for four-mode CV graph states

Characterized local Gaussian equivalence classes of CV graph states

Extended graph transformation rules to continuous-variable systems

Abstract

The local complementation rule is applied for continuous-variable (CV) graph states in the paper, which is an elementary graph transformation rule and successive application of which generates the orbit of any graph states. The corresponding local Gaussian transformations of local complementation for four-mode unweighted graph states were found, which do not mirror the form of the local Clifford unitary of qubit exactly. This work is an important step to characterize the local Gaussian equivalence classes of CV graph states.