Nonclassical nullifiers for quantum hypergraph states

TL;DR

This paper introduces criteria for detecting nonclassicality in quantum hypergraph states, analyzing their robustness and proposing experimental approaches to observe these states' nonclassical features.

Contribution

It develops necessary criteria for hypergraph nonclassicality based on nonlinear squeezing and analyzes their robustness in realistic experimental conditions.

Findings

Criteria for hypergraph nonclassicality based on nonlinear squeezing

Analysis of robustness against thermalisation and loss

Proposed experimental methods to observe nonclassicality

Abstract

Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve universality for continuous variable measurement based quantum computation with only Gaussian measurements. For normalised states, the simplest hypergraph states are formed from $k$-adic interactions among a collection of $k$ harmonic oscillator ground states. However such powerful resources have not yet been observed in experiments and their robustness and scalability have not been tested. Here we develop and analyse necessary criteria for hypergraph nonclassicality based on simultaneous nonlinear squeezing in the nullifiers of hypergraph states. We put forward an essential analysis of their robustness to realistic scenarios involving thermalisation or loss and suggest several basic proof-of-principle options for experiments to observe nonclassicality in hypergraph states.