Genuinely Multipartite Entanglement Vias Shallow Quantum Circuits. Issue 2 (9th December 2022) - Luo, Ming‐Xing; Fei, Shao‐Ming
Abstract: Multipartite entanglement is of important resources for quantum communication and quantum computation. The goal of this paper is to characterize general multipartite entangled states according to shallow quantum circuits. It is first proved that 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 has the smallest nontrivial circuit depth in the shallow quantum circuit model. Further, a semi‐device‐independent entanglement model depending on the local connection ability in the second layer of quantum circuits is proposed. 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. Abstract : Constant‐depth quantum circuits provide quantum advantage for 2D hidden linear function problem. Multipartite entanglement is characterized based on 2‐layer shallow quantum circuits of bipartite quantum channels. This shows different multipartite nonlocalities from the quantum network entanglement and implies a complete hierarchy of distinguishing genuinely multipartite entanglement.