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Fast Quantum Byzantine Agreement: Difference between revisions
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* Then each player sequentially executes two classical subroutines to bias the agreement value towards <math>0</math> or <math>1</math> (outcomes of a coin flip). This guarantees that if the non-faulty players are in agreement, then they will terminate and successfully output the correct agreement value <math>d</math> (not an outcome of coin flip). | * Then each player sequentially executes two classical subroutines to bias the agreement value towards <math>0</math> or <math>1</math> (outcomes of a coin flip). This guarantees that if the non-faulty players are in agreement, then they will terminate and successfully output the correct agreement value <math>d</math> (not an outcome of coin flip). | ||
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[[File:ByzantineAgreementFig.PNG| | [[File:ByzantineAgreementFig.PNG|50px|frame|Schematic representation of an execution of a Byzantine Agreement protocol with <math>n = 5</math> nodes and <math>t = 1</math> Byzantine failure. The red bits indicate the input value of each node, whereas the green bit represents the output. The solution shown satisfies the ''agreement'' and ''validity'' properties. The quantum Byzantine agreement protocol in the most strong model requires constant expected number of rounds, whereas a classical lower bound of <math>{\Omega}(\sqrt{n / \log(n)})</math> is known.]] | ||
'''[[Quantum Oblivious Common Coin]] subroutine:''' The heart of this protocol comes from the quantum enhanced [[Oblivious Common Coin]]. At the end of this subroutine, each player outputs a random bit, such that with a least probability value (called the [[fairness]]) <math>0</math> or <math>1</math>. Intuitively, this subroutines tosses a common coin, where all players get either heads or tails, each with fairness probability, but there may be executions where all players do not get the same output and no common coin is actually tossed. Since the players do not know whether the outcomes are all equal or not, this type of coin tossing is referred to as oblivious common coin tossing. In particular, using quantum resources, this task can be achieved in constant rounds (in the defined model). The implementation of this subroutine makes use of a weakened version of [[Verifiable Quantum Secret Sharing]] (VQSS). | '''[[Quantum Oblivious Common Coin]] subroutine:''' The heart of this protocol comes from the quantum enhanced [[Oblivious Common Coin]]. At the end of this subroutine, each player outputs a random bit, such that with a least probability value (called the [[fairness]]) <math>0</math> or <math>1</math>. Intuitively, this subroutines tosses a common coin, where all players get either heads or tails, each with fairness probability, but there may be executions where all players do not get the same output and no common coin is actually tossed. Since the players do not know whether the outcomes are all equal or not, this type of coin tossing is referred to as oblivious common coin tossing. In particular, using quantum resources, this task can be achieved in constant rounds (in the defined model). The implementation of this subroutine makes use of a weakened version of [[Verifiable Quantum Secret Sharing]] (VQSS). | ||