Genuinely Multipartite Entanglement vias Shallow Quantum Circuits

Abstract: Multipartite entanglement is of important resources for quantum communication and quantum computation. Our goal in this paper is to characterize general multipartite entangled states according to shallow quantum circuits. We firstly prove any genuinely multipartite entanglement on finite-dimensional spaces can be generated by using 2-layer shallow quantum circuit consisting of two biseparable quantum channels, which the smallest nontrivial circuit depth in the shallow quantum circuit model. We further propose a semi-device-independent entanglement model depending on the local connection ability in the second layer of quantum circuits. This implies a complete hierarchy of distinguishing genuinely multipartite entangled states. It shows a completely different multipartite nonlocality from the quantum network entanglement. These results show new insights for the multipartite entanglement, quantum network, and measurement-based quantum computation.