Universality of Generalized Bunching and Efficient Assessment of Boson Sampling

TL;DR

This paper reveals universal properties of bosons and fermions in linear networks, enabling efficient certification of boson sampling devices' quantum coherence with polynomial resources.

Contribution

It establishes the universality of generalized bunching/antibunching and introduces a polynomial-time certification protocol for boson sampling.

Findings

Maximal detection probabilities occur only for indistinguishable particles.

Certification protocol is polynomial in the number of particles.

Analytic formulas are provided for scattershot boson sampling.

Abstract

It is found that identical bosons (fermions) show generalized bunching (antibunching) property in linear networks: The absolute maximum (minimum) of probability that all $N$ input particles are detected in a subset of $\mathcal{K}$ output modes of any nontrivial linear $M$-mode network is attained \textit{only} by completely indistinguishable bosons (fermions). For fermions $\mathcal{K}$ is arbitrary, for bosons it is either ($i$) arbitrary for only classically correlated bosons or ($ii$) satisfies $\mathcal{K}\ge N$ (or $\mathcal{K}=1$) for arbitrary input states of $N$ particles. The generalized bunching allows to certify in a \textit{polynomial} in $N$ number of runs that a physical device realizing Boson Sampling with \textit{an arbitrary} network operates in the regime of full quantum coherence compatible \textit{only} with completely indistinguishable bosons. The protocol needs \textit{only polynomial} classical computations for the standard Boson Sampling, whereas an \textit{analytic formula} is available for the scattershot version.