Semi-device-independent characterisation of multipartite entangled states and measurements

TL;DR

This paper introduces a semi-device-independent method for certifying multipartite entanglement and entangled measurements in quantum systems, robust against noise and applicable to states with local models.

Contribution

It presents a novel semi-device-independent scheme for certifying genuine multipartite entanglement and entangled measurements with minimal device assumptions.

Findings

Certifies high-dimensional multipartite entanglement.

Provides lower bounds on entangled measurement operators.

Robust to noise and optimal for certain states.

Abstract

The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterisation of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterised beyond an assumption about the dimension of their Hilbert spaces. Our scheme can certify that an $n$-partite high-dimensional quantum state features genuine multipartite entanglement. Moreover, the scheme can certify that a joint measurement on $n$ subsystems is entangled, and provides a lower bound on the number of entangled measurement operators. These tests are strongly robust to noise, and even optimal for certain classes of states and measurements, as we demonstrate with illustrative examples. Notably, our scheme allows for the certification of many entangled states admitting a local model, which therefore cannot violate any Bell inequality.