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Multi-partite Quantum Entanglement versus Randomization: Fair and Unbiased Leader Election in Networks

Sudebkumar Prasant Pal·Sudhir Kumar Singh·Somesh Kumar
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Abstract

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.

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Sudebkumar Prasant Pal, Sudhir Kumar Singh, Somesh Kumar. 2003-06-29. Multi-partite Quantum Entanglement versus Randomization: Fair and Unbiased Leader Election in Networks. https://arxiv.org/abs/quant-ph/0306195

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