【研究进展】国防科大徐平课题组：通过频率梳和图论产生紧凑型GHZ态
【View&Perspective】
通过频率梳和图论产生紧凑型GHZ态
Xuemei Gu1,†, Mario Krenn2,‡1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
E-mail: xmgu@ustc.edu.cn
2Department of Chemistry & Computer Science, University of Toronto, Toronto, ON, M5S 3H6, Canada;Vector Institutefor Artificial Intelligence, Toronto, ON, M5S 1M1, CanadaE-mail: mario.krenn@univie.ac.at量子纠缠是量子物理学预言的最令人费解的现象之一。它认为，两个粒子之间可以相互作用，对其中一个粒子进行观测可以即时地影响到其它粒子，无论它们之间的距离有多远。爱因斯坦对此难以置信，并称这一现象是“幽灵般的远距效应”[1]。在20世纪60年代，约翰·贝尔证明了量子力学确实与我们的经典世界观发生了冲突，后者是局部的（信息可以以光速最大限度地传输）和现实的（属性存在于测量之前，并且与测量无关)[2]。在接下来的50年里，实验学家进一步证实了量子力学的预言，并且在更加严格的测量中排除了局域的现实世界观[3-8]。
在20世纪80年代末，Daniel Greenberger、Michael Horne和Anton Zeilinger（简称GHZ）提出了这样一个问题：如果纠缠中涉及的不是两个，而是三个粒子，会发生什么？值得注意的是，他们发现对局域现实主义理论的排斥不仅仅是一种统计预测，而且可以在“全无”的测量中观察到。这个结果现在被称为GHZ定理，在某种意义上是对经典理论最有力的否定[9,10]。
GHZ态，如
光子技术是实现这一目标的主要路线之一。比如我们可以使用n个概率光子对源（如非线性晶体）来系统地实现2n个偏振光子GHZ态。这些晶体与偏振分束器相结合，用来消除光子产生于哪一个晶体的信息。近年来，许多令人印象深刻的实验被相继报道[13-17]，最新的技术已经能将12个光子纠缠在一起，使得它们处于所有光子水平极化或所有光子垂直极化的相干叠加（想象一下这是多么迷人！）[18]。
如果要获得更大规模的GHZ状态，则实验硬件会相应地增加。实际上这并不令人惊讶，并且它似乎是很直观的，如果人们想要使用更多的光子对，则需要使用大量的光子对源，如图1(a)所示。
这正是国防科技大学徐平等人[20]研究产生的最新结果不同之处。他们提出了一种在不增加实验装置中光学元件数量的情况下，增加GHZ状态大小的方案。光子在偏振中纠缠，但不是在空间路径上来区分它们[21,22]，而是通过频率来区分光子。该提案中的关键要素是微环谐振器（MRR），它允许频率梳具有精确地间隔开的数百条尖锐线，并在大量频率仓之间建立相关性[19,23,24]。在这项令人印象深刻的新技术中，由于微环谐振器内部自发的四波混频过程中的能量守恒，因此产生了以泵浦光的光谱模式为中心的频率相关的光子对，如图1(b)所示。
作者利用这项技术，并将其与另一个新的理论概念相结合：光量子实验与图论之间的映射，这是我们（与Erhard和Zeilinger一起）在三年前的工作里提出的[25,26]，这已经成为设计和分析光量子纠缠和新量子光学装置的便捷工具[27-29]。
在原映射中，每个顶点代表一个可区分的光子模式，通常是光子的路径，但在徐平等人的提议中，它代表离散频率模式。两个顶点之间的边代表相关联的光子对。在这种情况下，边的颜色代表光子的偏振（蓝色表示水平偏振，即|0>，而红色表示垂直偏振，即|1>）。量子态（在每个频率模式下都以光子为条件）可以计算为图中所有完美匹配的相干叠加。图的完美匹配是一个边的子集，使得每个顶点都包含一次。在这种情况下，GHZ是一个简单的循环图，具有偶数个顶点和边，颜色交替（蓝色和红色）。
作者的聪明见解如下：他们观察到，只要三个微环谐振器就可以创建任意大小的GHZ状态图。前两个创建具有交替颜色的边的线性图，最后的微环谐振器连接了线性图的两端。图的大小也即GHZ态的大小，现在只取决于来自前两个微环谐振器的相关模式的数量，如图1(c)所述。作者还展示了如何基于我们光量子实验的超图推广[30]，将弱相干激光和概率源一起用于创建GHZ态。同样地，在他们的方案中，能够保证在不增加实验装置复杂性的情况下增加GHZ状态下的光子数量，如图1(d)所示。
话虽如此，该方案是基于概率光子源的，因此要创建2n个光子GHZ态，我们需要产生n对事件。扩展到更高的数目是困难的：如果创建一个光子对的概率是p，那么创建n对的概率是pn。概率p不能任意大，因为多光子事件会产生噪声。低损耗的光学元件、高效的光子探测器或光子数可分辨探测器可以有助于将n增加到较高值。
综上所述，受图论和实验的联系的启发，徐平等人提出的方案是令人惊讶和有趣的，为量子实验技术提供了一个新的视角。在未来的研究中，有几个问题也许会引起人们的兴趣。首先也是最重要的一点是，这个方案在实际实验中是否可行？特别是，三个微环谐振器是否可以以一种一致的方式组合，并且不同频率仓中不相等的生产概率会有什么影响？第二，到目前为止，作者已经演示了如何有效地生成GHZ状态。了解他们的想法在多大程度上可以扩展到寻找更通用图形的高效光学实现，这将非常有用。它们能推广到高维量子系统吗[31-33]？最近，加权彩色图用于新量子实验的人工智能设计已经被提出[34]。在那里，该算法以图形的形式提出了更多通用的实验解决方案。因此，对这里提出的观点的概括可以有广泛的实际应用。当然，我们期望在不久的将来会有更多激动人心的发展。
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扫码下载PDF全文:
Pingyu Zhu, Qilin Zheng, Shichuan Xue, Chao Wu, Xinyao Yu, Yang Wang, Yingwen Liu, Xiaogang Qiang, Junjie Wu, and Ping Xu, On-chip multiphoton Greenberger-Horne-Zeilinger state based on integrated frequency combs, Front. Phys. 15(6), 61501 (2020)（selected for the front cover）
Xuemei Gu and Mario Krenn, Compact Greenberger–Horne–Zeilinger state generation via frequency combs and graph theory, Front. Phys. 15(6), 61502 (2020)
Cover story: The Greenberger–Horne–Zeilinger (GHZ) serves as a fundamental resource for quantum applications. Always O(n) nonlinear sources are set for the generation of an n-qubit GHZ state, with strict coherence conditions. Here the authors propose an ultra-integrated scalable scheme to increase the size of GHZ states without increasing the number of optical elements, based on the frequency combs and graph theory. Frequency combs from just three on-chip micro-ring resonators can efficiently construct arbitrary GHZ states. Moreover, frequency-labeled photons of the final state lie in a single path that have significant potentials for long-distance quantum tasks. For more details, please refer to the article entitled “On-chipmultiphoton Greenberger–Horne–Zeilinger state based on integrated frequencycombs” by Pingyu Zhu,et al., Front. Phys. 15(6), 61501 (2020). [Photo credits: Ping Xu at National University of Defense Technology.]
Frontiers of Physics (FOP，IF 2.502)是由教育部发起、高教社出版、Springer海外发行的Frontiers系列英文学术期刊之一，旨在报道国际物理学领域的最新成果和研究进展，主要发表Topical Review、Review、Research Article、View & Perspective、Research Highlight，也委托专家组织特定前沿主题的专题。现任总主编：赵光达院士；执行主编：李定平教授；主编：龙桂鲁教授（量子计算与量子信息）、张卫平教授（AMO）、王楠林教授（凝聚态与材料物理）、李海波教授（核物理/粒子物理/天体物理与宇宙学）。期刊已被SCI, JCR, ADS, SCOPUS, INSPEC, Google Scholar, CSCI, CSCD等收录。2013-2018入选中国科技期刊提升计划资助项目，2019年入选中国科技期刊卓越行动计划资助项目。详细请扫码关注：
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