Gulbahar Burhan
Department of Electrical and Electronics Engineering, Ozyegin University, Istanbul 34794, Turkey.
Entropy (Basel). 2020 Feb 21;22(2):246. doi: 10.3390/e22020246.
Quantum history states were recently formulated by extending the consistent histories approach of Griffiths to the entangled superposition of evolution paths and were then experimented with Greenberger-Horne-Zeilinger states. Tensor product structure of history-dependent correlations was also recently exploited as a quantum computing resource in simple linear optical setups performing multiplane diffraction (MPD) of fermionic and bosonic particles with remarkable promises. This significantly motivates the definition of quantum histories of MPD as entanglement resources with the inherent capability of generating an exponentially increasing number of Feynman paths through diffraction planes in a scalable manner and experimental low complexity combining the utilization of coherent light sources and photon-counting detection. In this article, quantum temporal correlation and interference among MPD paths are denoted with quantum path entanglement (QPE) and interference (QPI), respectively, as novel quantum resources. Operator theory modeling of QPE and counterintuitive properties of QPI are presented by combining history-based formulations with Feynman's path integral approach. Leggett-Garg inequality as temporal analog of Bell's inequality is violated for MPD with all signaling constraints in the ambiguous form recently formulated by Emary. The proposed theory for MPD-based histories is highly promising for exploiting QPE and QPI as important resources for quantum computation and communications in future architectures.
量子历史态最近通过将格里菲斯的一致历史方法扩展到演化路径的纠缠叠加而被提出，随后在格林伯格 - 霍恩 - 蔡林格态上进行了实验。历史相关关联的张量积结构最近也在简单的线性光学装置中被用作量子计算资源，该装置对费米子和玻色子粒子进行多平面衍射（MPD），具有显著前景。这极大地推动了将MPD的量子历史定义为纠缠资源，其具有以可扩展方式通过衍射平面生成指数级增加数量的费曼路径的内在能力，并且结合了相干光源的利用和光子计数检测，实验复杂度较低。在本文中，MPD路径之间的量子时间关联和干涉分别被表示为量子路径纠缠（QPE）和干涉（QPI），作为新型量子资源。通过将基于历史的公式与费曼路径积分方法相结合，给出了QPE的算符理论建模和QPI的反直觉性质。对于最近由埃马里以模糊形式提出的所有信号约束下的MPD，违反了作为贝尔不等式时间类似物的莱格特 - 加尔不等式。所提出的基于MPD历史的理论对于将QPE和QPI作为未来架构中量子计算和通信的重要资源加以利用具有很大前景。
