Title: Universal Bound on Sampling Bosons in Linear Optics Show Chinese title

Title: 线性光学中采样玻色子的通用界

Abstract: In linear optics, photons are scattered in a network through passive optical elements including beamsplitters and phase shifters, leading to many intriguing applications in physics, such as Mach-Zehnder interferometry, Hong-Ou-Mandel effect, and tests of fundamental quantum mechanics. Here we present a general analytic expression governing the upper limit of the transition amplitudes in sampling bosons, through all realizable linear optics. Apart from boson sampling, this transition bound results in many other interesting applications, including behaviors of Bose-Einstein Condensates (BEC) in optical networks, counterparts of Hong-Ou-Mandel effects for multiple photons, and approximating permanents of matrices. Also, this general bound implies the existence of a polynomial-time randomized algorithm for estimating transition amplitudes of bosons, which represents a solution to an open problem raised by Aaronson and Hance in 2012. Show Chinese abstract

Abstract: 在线性光学中，光子通过包括分束器和相位移器在内的无源光学元件在网络中散射，从而在物理领域产生许多引人入胜的应用，例如马赫-曾德尔干涉仪、洪-欧-曼德尔效应以及基础量子力学的测试。 在这里，我们给出了一个通用的解析表达式，用于控制在线性光学中采样玻色子时过渡振幅的上限。除了玻色子采样之外，这个过渡界值还导致了许多其他有趣的应用，包括光学网络中玻色-爱因斯坦凝聚态（BEC）的行为、多光子的洪-欧-曼德尔效应的对应物以及矩阵的永久值近似。 此外，这个通用界值暗示了存在一个用于估计玻色子过渡振幅的多项式时间随机算法，这解决了亚伦森和汉斯在2012年提出的开放问题。