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

Abstract: The detection of genuine multipartite entanglement (GME) is a state-characterization task that can be viewed as a benchmark in that it confirms appropriate levels of coherence and the ability to control the system in the laboratory. However, many GME tests require joint measurements on all or the majority of the involved quantum systems, posing experimental challenges for platforms with restricted qubit connectivity such as typical setups for time-bin encoded qubits. Here we construct a family of versatile GME criteria that only require measurements of a small subset, i.e., $O(n^2)$ out of $2^n$, of (at most) $m$-body stabilizers of $n$-qubit target graph states, with $m$ bounded from above by twice the maximum degree of the underlying graph. We present analytical results for white-noise-added graph states and numerical simulations for graph states produced in microwave photonic qubits that demonstrate the versatility and performance of our GME criteria under realistic conditions.