Remote Sampling with Applications to General Entanglement Simulation

TL;DR

This paper introduces a method for exact remote sampling of probability distributions using a distributed version of von Neumann's rejection algorithm, with applications to simulating complex quantum entanglement scenarios efficiently.

Contribution

It develops a distributed sampling protocol based on rejection sampling and applies it to simulate general quantum entanglement among multiple parties.

Findings

Expected communication cost is O(m^2) bits for bounded dimensions and outcomes.

Trade-off between rounds of rejection algorithm and communication bits.

Protocol enables exact simulation of quantum measurements in multi-party systems.

Abstract

We show how to sample exactly discrete probability distributions whose defining parameters are distributed among remote parties. For this purpose, von Neumann's rejection algorithm is turned into a distributed sampling communication protocol. We study the expected number of bits communicated among the parties and also exhibit a trade-off between the number of rounds of the rejection algorithm and the number of bits transmitted in the initial phase. Finally, we apply remote sampling to the simulation of quantum entanglement in its most general form possible, when an arbitrary number of parties share systems of arbitrary dimensions on which they apply arbitrary measurements (not restricted to being projective measurements). In case the dimension of the systems and the number of possible outcomes per party is bounded by a constant, it suffices to communicate an expected O(m^2) bits in order to simulate exactly the outcomes that these measurements would have produced on those systems, where m is the number of participants.