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arXiv 1807.06649quant-phcs.ITmath.IT
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远程采样及其在一般纠缠模拟中的应用

Remote Sampling with Applications to General Entanglement Simulation

Gilles Brassard, Luc Devroye, Claude Gravel

摘要:

我们展示了如何准确地采样离散的概率分布,其定义参数分布在远程方。为此,冯诺依曼的拒绝算法变成了一个分布式采样通信协议。我们研究了各方之间通信的比特的预期数量,并且还表现出拒绝算法的轮数和在初始阶段传输的比特数之间的权衡。最后,我们应用远程采样的量子纠缠在其最一般的形式可能的模拟,当任意数量的各方共享系统的任意尺寸上,他们应用任意测量(不限于投影测量)。如果系统的维数和每一方可能的结果数都是一个常数,那么为了精确地模拟这些测量在这些系统上产生的结果,只需要传递一个预期的O(m^2)比特就足够了,其中m是参与者的数量。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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