Zhang Da, Barral David, Cai Yin, Zhang Yanpeng, Xiao Min, Bencheikh Kamel
Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Centre de Nanosciences et de Nanotechnologies C2N, CNRS, Université Paris-Saclay, 91120 Palaiseau, France.
Phys Rev Lett. 2021 Oct 8;127(15):150502. doi: 10.1103/PhysRevLett.127.150502.
The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate high-order Hamiltonians remains unclear. Here, we derive a hierarchy of sufficient and necessary conditions for the positive-partial-transposition separability of bipartite nonlinear quantum states. The proposed criteria detect the nonpositive-partial-transposition inseparability of higher-order moments of states, which provides a systematic framework for the characterization of this kind of entanglement. Through numerical simulation of cubic and quartic Hamiltonians, we demonstrate the existence and competition of a hierarchy of entanglement witnesses, revealing the mechanism underlying such entanglement. Our results may provide a new direction in continuous variable quantum information processing.
双线性哈密顿量在连续变量中产生的纠缠已得到深入研究并被广泛应用。相比之下，由部分简并高阶哈密顿量描述的非线性相互作用所产生的纠缠物理仍不明确。在此，我们推导了二分非线性量子态正偏置转置可分性的一系列充分必要条件。所提出的判据检测态的高阶矩的非正偏置转置不可分离性，这为表征此类纠缠提供了一个系统框架。通过对三次和四次哈密顿量的数值模拟，我们证明了纠缠见证者层级的存在与竞争，揭示了此类纠缠的潜在机制。我们的结果可能为连续变量量子信息处理提供一个新方向。
