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Paper IPM / P / 15891  


Abstract:  
We introduce a method for efficient, in situ characterization of linearoptical networks (LONs) in randomized bosonsampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share twomode squeezedvacuum 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. 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 twomode squeezedvacuum states: the entanglement allows Alice to choose for each run of the experiment between RBS and a simple characterization protocol based on firstorder coherence.
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