# Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements

## TL;DR

This paper introduces a new method to detect genuine multipartite entanglement in quantum systems using limited measurements, making it easier to benchmark quantum devices.

## Contribution

The paper introduces versatile GME and k-inseparability criteria requiring only few-body measurements on multi-qubit states.

## Key findings

- The proposed criteria require measuring only O(n²) stabilizers instead of all 2ⁿ stabilizers.
- The method is noise-robust and applicable to photonic and superconducting graph states.
- Semidefinite programming reduces the number or weight of required stabilizers.

## Abstract

Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges for systems like time-bin encoded qubits and microwave photons from superconducting circuits, where qubit connectivity is limited or measurement noise grows with the number of jointly measured qubits. Here we introduce versatile GME and k-inseparability criteria applicable to any state, which only require measuring O(n2) out of 2n (at most) m-body stabilizers of n-qubit target graph states, with m upper-bounded by twice the graph’s maximum degree. For cluster or ring-graph states, only constant-weight stabilizers are needed. Using semidefinite programming (and sometimes graph-local complementations), we can reduce the number or weight of required stabilizers. Analytical and numerical results show that our criteria are noise-robust and may infer state infidelity from certified k-inseparability in microwave photonic graph states generated under realistic conditions.

Certifying multipartite entanglement can benchmark quantum devices. Here, authors introduce versatile tests that can certify genuine multipartite entanglement and k-inseparability using only few-body measurements, enabling noise-robust benchmarking of large photonic and superconducting graph states.