多体量子纠缠与随机化：网络中公平无偏的领导选举
Multi-partite Quantum Entanglement versus Randomization: Fair and Unbiased Leader Election in Networks
摘要：
在本文中，我们表明，充分的多方量子纠缠有助于公平和公正的选举中的领导者在一个分布式网络的处理器，只有线性经典通信的复杂性。我们发现，一个总的$O(\log n)$不同的多方最大纠缠集（ebits）能够支持这样的协议中存在的节点，可能会说谎，从而被偏见。这里，$n$是网络中节点的数量。我们还证明了在没有量子纠缠的情况下，即使所有节点都有完美的随机比特发生器，也很难执行无偏和公平的选举具有线性经典通信复杂性的领导者。我们发现，存在足够数量的$O(n/\log n)$的有偏见的代理人导致一个非零的限制概率的领导者有偏见的选举，而存在的一个较小的数量$O(\log n)$的有偏见的代理人无关紧要。我们定义了两个新的相关的复杂性类的动机，我们的领导人选举问题，并讨论了一些开放的问题。
英文摘要：
In this paper we show that sufficient multi-partite quantum entanglement helps in fair and unbiased election of a leader in a distributed network of processors with only linear classical communication complexity. We show that a total of $O(\log n)$ distinct multi-partite maximally entanglement sets (ebits) are capable of supporting such a protocol in the presence of nodes that may lie and thus be biased. Here, $n$ is the number of nodes in the network. We also demonstrate the difficulty of performing unbiased and fair election of a leader with linear classical communication complexity in the absence of quantum entanglement even if all nodes have perfect random bit generators. We show that the presence of a sufficient number $O(n/\log n)$ of biased agents leads to a non-zero limiting probability of biased election of the leader, whereas, the presence of a smaller number $O(\log n)$ of biased agents matters little. We define two new related complexity classes motivated by the our leader election problem and discuss a few open questions.
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。
