Beckey Jacob L, Gigena N, Coles Patrick J, Cerezo M
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
JILA, NIST and University of Colorado, Boulder, Colorado 80309, USA.
Phys Rev Lett. 2021 Oct 1;127(14):140501. doi: 10.1103/PhysRevLett.127.140501.
Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state |ψ⟩ for these applications is often directly related to the degree or type of entanglement present in |ψ⟩. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called concentratable entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under local operations and classical communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.
多方纠缠是量子通信、量子计算、量子传感和量子网络的重要资源。量子态|ψ⟩在这些应用中的效用通常与|ψ⟩中存在的纠缠程度或类型直接相关。因此，有效地量化和表征多方纠缠至关重要。在这项工作中，我们引入了一族多方纠缠度量，称为可浓缩纠缠。几个著名的纠缠度量作为我们这族度量的特殊情况被恢复，因此我们提供了一个量化多方纠缠的通用框架。我们证明，在局部操作和经典通信下，整个族平均不会增加。我们还根据纠缠到贝尔对的概率浓缩为这些度量提供了一个操作意义。最后，我们表明通过实施并行化的SWAP测试，可以在量子计算机上有效地估计这些量，从而为在量子设备上测量多方纠缠开辟了一个研究方向。
