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Quantum Entanglement and Communication Complexity
We consider a variation of the multi-party communication complexity scenario
where the parties are supplied with an extra resource: particles in an
entangled quantum state. We show that, although a prior quantum entanglement
cannot be used to simulate a communication channel, it can reduce the
communication complexity of functions in some cases. Specifically, we show
that, for a particular function among three parties (each of which possesses
part of the function's input), a prior quantum entanglement enables them to
learn the value of the function with only three bits of communication occurring
among the parties, whereas, without quantum entanglement, four bits of
communication are necessary. We also show that, for a particular two-party
probabilistic communication complexity problem, quantum entanglement results in
less communication than is required with only classical random correlations
(instead of quantum entanglement). These results are a noteworthy contrast to
the well-known fact that quantum entanglement cannot be used to actually
simulate communication among remote parties.Comment: 10 pages, latex, no figure
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