Quantum Entanglement and the Communication Complexity of the Inner Product Function

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  • 11 August 1997
Abstract
We consider the communication complexity of the binary inner product function in a variation of the two-party communication complexity scenario where the parties have an a priori supply of particles in an entangled quantum state. Previous proofs of lower bounds for the inner product function exist in scenarios where there is no initial entanglement, but they do not apply in the scenario with prior entanglement. In fact, there exist functions whose communication complexity with prior entanglement is provably less than that in models of communication without entanglement. We show that the communication complexity of the inner product function with prior entanglement is at least n/2. Our proof employs a novel kind of ``quantum'' reduction between protocols.

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