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Are there any distributed consensus protocols which make use of quantum phenomena for improved performance? For example, symmetry breaking with a shared quantum state.

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In addition to the mentioned papers, there has been some interesting research efforts in designing Quantum Distributed Consensus Algorithms. In one of the early approaches, Ellie D’Hondt and Prakash Panangaden has designed a Quantum Distributed Consensus Algorithm using the distinctive properties of W-State and GHZ-state systems. It is detailed in the following research paper. This paper outlines the state computation of quantum processors participating in the distributed consensus through a sequence of symmetric moves in the anonymous network.

As per this approach, in an anonymous network if the processors share the W -state then a trivial protocol allows them to solve the leader election problem. Similarly the GHZ-state is the only shared quantum resource that allows solution of distributed consensus. It has devised these state based quantum processors to realise a Quantum Leader Election and Quantum Distributed Consensus in an anonymous network.

The W state is one of the two non-biseparable classes of three-qubit states (the other being the GHZ state), which cannot be transformed into each other by local quantum operations. Thus W and GHZ represent two very different kinds of tripartite entanglement. This property is quite useful in constructing unique local views of quantum states among processors participating in the distributed consensus. It is also quite efficient to construct quantum distributed network state among the participants in the consensus. The emergence of GHZ state and W state in this consensus algorithm has definite role in the symmetry breaking state transitions and state termination events.

There is another relevant approach is proposed by Bogdan S. Chlebus, Dariusz R. Kowalski and Michał Strojnowski in the the following journal. This algorithm seems to be attempting a scalable quantum Consensus for crash failures, essentially focusing on designing a CFT consensus algorithm. One interesting aspect of this paper is that it factors the impact of quantum adversaries in a distributed consensus context. It is also attempting a randomised approach to arrive at the eventual finality.

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