Remote Sampling with Applications to General Entanglement Simulation

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.

arXiv comment17 pages, 1 figure, 4 algorithms (protocols); Complete generalization of previous paper arXiv:1303.5942 [cs.IT] -- Exact simulation of the GHZ distribution -- by the same authors

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Cited by in corpus (5)

• Classical Cost of Transmitting a Qubit
• Neural Network Approach to the Simulation of Entangled States with One Bit of Communication
• The minimal communication cost for simulating entangled qubits
• Quantum Communication -- Celebrating the Silver Jubilee of Teleportation
• Beating one bit of communication with quantum correlations in smaller dimensions