Editing Fast Quantum Byzantine Agreement (section)

==Properties==
The protocol
* solves the problem in <math>O(1)</math> expected number of rounds, in particular independent of <math>n</math> and <math>t</math>, whereas classically a lower bound of <math>\Omega\left(\sqrt{n / \log(n)}\right)</math> is known [[Quantum Byzantine Agreement#References|(3), (6)]];
* tolerates <math>t \leq n/3</math> (synchronous) or <math>t \leq n/4</math> (asynchronous) Byzantine failures;
* reaches ''agreement'' (each player outputs the same bit) under the ''validity'' condition (the agreement value was proposed by at least one player) and is guaranteed to ''terminate eventually'' (infinite executions occur almost never - i.e. have probability measure zero).

The Quantum Oblivious Common Coin subroutine has a single parameter <math>k</math> (used in the [[Verifiable Quantum Secret Sharing scheme]]), but it is unclear from the works [[Quantum Byzantine Agreement#References|(1), (3)]] how the parameter <math>k</math> influences the guarantees of the protocol. 

Also note that the fairness <math>p</math> of the Quantum Oblivious Common Coin is not a parameter, but rather a result of the specific implementation of the protocol. The global Byzantine Agreement protocol can then tolerate up to <math>t < \left \lfloor{pn}\right \rfloor </math> failures. The Quantum Oblivious Common Coin subroutine proposed by [[Quantum Byzantine Agreement#References|(3)]] has <math>p > 1/3</math> (synchronous case, <math>p > 1/4</math> asynchronous case).