Sufficient Conditions for Efficient Classical Simulation of Quantum Optics

TL;DR

This paper establishes practical criteria based on phase-space quasiprobability distributions for efficiently classically simulating quantum optics experiments, especially boson sampling, by analyzing the effects of imperfections like noise and mode mismatching.

Contribution

It introduces new sufficient conditions for classical simulation of quantum optics experiments using phase-space negativity, aiding the assessment of experimental imperfections.

Findings

Conditions for classical simulability based on PQD negativity

Thresholds for noise and loss where boson sampling becomes classically simulatable

Mode mismatching identified as a major source of simulation-breaking errors

Abstract

We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process. We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling. In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors. Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable. We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.