Universal Bound on Sampling Bosons in Linear Optics

TL;DR

This paper derives a universal upper bound on transition amplitudes in linear optical boson sampling, with implications for quantum physics applications and a polynomial-time algorithm for amplitude estimation.

Contribution

It provides the first general analytic bound on bosonic transition amplitudes in linear optics, enabling new applications and solving an open problem in quantum computing.

Findings

Derived a universal bound on bosonic transition amplitudes.

Introduced a polynomial-time randomized algorithm for amplitude estimation.

Connected the bound to various quantum phenomena and computational problems.

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.