Liars, Byzantines, and Generals

It seems some folks at the the Max Planck Institute for Quantum Optics have developed a quantum communication protocol whereby they can utilize entangled qubits – photons in this case – to detect the fault or liar in a three-party communication system.  This is an example of a what is sometimes called a consensus problem.  Specifically, this is known as a Byzantine agreement which is a more general example of the famous Two Generals’ Problem.  It’s a fairly complex problem, but essentially provides a means for parties to agree on certain points.  In any case, in the quantum Byzantine problem, since there are three parties (call them Alice, Bob, and Charlie), the trick has been finding a way to implement it since the primary benefit of quantum mechanics is that it provides entangled pairs of qubits.  Note that qubits are inherently binary – they have two states by definition.  In the Byzantine problem one might think a qutrit – a three-state particle – would be best and indeed it certainly would be helpful.  But qutrits are difficult to realize experimentally.  Thus the group at Max Planck has found another way to do it.  They instead use four entangled photons (qubits) to accomplish the task.  I’ve oversimplified things here, but encourage the interested reader to follow the links to more detailed descriptions.  As a note, a pre-print of their paper is here.  And, if you’ve got 50 minutes to blow, check out this Google TechTalk on the Byzantine Agreement (among other things).

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