Quantum Entanglement and Communication Complexity

Abstract

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.