Gu Xuemei, Erhard Manuel, Zeilinger Anton, Krenn Mario
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 1090 Vienna, Austria;
State Key Laboratory for Novel Software Technology, Nanjing University, 210023 Nanjing City, China.
Proc Natl Acad Sci U S A. 2019 Mar 5;116(10):4147-4155. doi: 10.1073/pnas.1815884116. Epub 2019 Feb 15.
We present an approach to describe state-of-the-art photonic quantum experiments using graph theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. This viewpoint immediately leads to many interesting results, some of which we present here. First, we identify an experimental unexplored multiphoton interference phenomenon. Second, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Third, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights into quantum state generation with current photonic technology. Fourth, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and graph theory offers another perspective on a widely used technology and immediately raises many follow-up questions.
我们提出了一种使用图论来描述前沿光子量子实验的方法。在该方法中，量子态由完美匹配的相干叠加给出。关键的发现是，在图中引入复数权重自然会导致量子干涉。这一观点立即产生了许多有趣的结果，我们在此展示其中一些。首先，我们识别出一种尚未被实验探索的多光子干涉现象。其次，我们发现计算此类实验的结果是#P-难问题，这意味着它是一个处理矩阵函数“积和式”及其推广“哈夫尼亚多项式”计算的经典难处理问题。第三，我们解释了最近的一个不可行结果如何普遍适用于线性光学量子实验，从而揭示了当前光子技术在量子态生成方面的重要见解。第四，我们展示了如何以图形方式描述诸如纠缠交换等量子协议。量子实验与图论之间发现的桥梁为一种广泛使用的技术提供了另一个视角，并立即引发了许多后续问题。
