Agustí A, Chang C W Sandbo, Quijandría F, Johansson G, Wilson C M, Sabín C
Instituto de Física Fundamental, CSIC, Serrano, 113-bis, 28006 Madrid, Spain.
Institute for Quantum Computing and Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Phys Rev Lett. 2020 Jul 10;125(2):020502. doi: 10.1103/PhysRevLett.125.020502.
We show that the states generated by a three-mode spontaneous parametric down-conversion (SPDC) interaction Hamiltonian possess tripartite entanglement of a different nature to other paradigmatic three-mode entangled states generated by the combination of two-mode SPDC interactions. While two-mode SPDC generates Gaussian states whose entanglement can be characterized by standard criteria based on two-mode quantum correlations, these criteria fail to capture the entanglement generated by three-mode SPDC. We use criteria built from three-mode correlation functions to show that the class of states recently generated in a superconducting-circuit implementation of three-mode SPDC ideally have tripartite entanglement, contrary to recent claims in the literature. These criteria are suitable for triple SPDC but we show that they fail to detect tripartite entanglement in other states which are known to possess it, which illustrates the existence of two fundamentally different notions of tripartite entanglement in three-mode continuous-variable systems.
我们表明，由三模自发参量下转换（SPDC）相互作用哈密顿量产生的态具有一种与通过双模SPDC相互作用组合产生的其他典型三模纠缠态不同性质的三方纠缠。虽然双模SPDC产生的高斯态的纠缠可以通过基于双模量子关联的标准判据来表征，但这些判据无法捕捉三模SPDC产生的纠缠。我们使用基于三模关联函数构建的判据来表明，最近在三模SPDC的超导电路实现中产生的态类理想地具有三方纠缠，这与文献中最近的说法相反。这些判据适用于三重SPDC，但我们表明它们无法检测出已知具有三方纠缠的其他态中的三方纠缠，这说明了在三模连续变量系统中存在两种根本不同的三方纠缠概念。
