In situ characterization of linear-optical networks in randomized boson sampling

TL;DR

This paper presents an in situ method for characterizing linear-optical networks in randomized boson sampling experiments using entangled states, enabling efficient assessment of losses without disrupting the experiment.

Contribution

The authors introduce a novel protocol leveraging entanglement for real-time, in situ characterization of lossy linear-optical networks in boson sampling.

Findings

The method allows in situ characterization without changing Bob's setup.

Fidelity bounds provide a measure of how losses affect the sampling distribution.

Entanglement enables switching between sampling and characterization modes.

Abstract

We introduce a method for efficient, in situ characterization of linear-optical networks (LONs) in randomized boson-sampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share two-mode squeezed-vacuum states. In this protocol, Alice performs local measurements on her modes, either photon counting or heterodyne. Bob implements and applies to his modes the LON requested by Alice; at the output of the LON, Bob performs photon counting, the results of which he sends to Alice via classical channels. In the ideal situation, when Alice does photon counting, she obtains from Bob samples from the probability distribution of the RBS problem, a task that is believed to be classically hard to simulate. When Alice performs heterodyne measurements, she converts the experiment to a problem that is classically efficiently simulable, but more importantly, enables her to characterize a lossy LON on the fly, without Bob's knowing and without changing anything at Bob's end (this is what we mean by in situ). We introduce and calculate the fidelity between the joint states shared by Alice and Bob after the ideal and lossy LONs as a measure of distance between the two LONs. Using this measure, we obtain an upper bound on the total variation distance between the ideal probability distribution for the RBS problem and the probability distribution achieved by a lossy LON. Our method displays the power of the entanglement of the two-mode squeezed-vacuum states: the entanglement allows Alice to choose for each run of the experiment between RBS and a simple characterization protocol based on first-order coherence between complex amplitudes.