paper

Interaction in Quantum Communication

arXiv:quant-ph/0603135 · doi:10.1109/TIT.2007.896888

Abstract

In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges between the communicating parties. It is therefore natural to ask whether every classical protocol may be transformed to a ``simpler'' quantum protocol--one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity. This, in particular, proves a round hierarchy theorem for quantum communication complexity, and implies, via a simple reduction, an Omega(N^{1/k}) lower bound for k message quantum protocols for Set Disjointness for constant k. Enroute, we prove information-theoretic lemmas, and define a related measure of correlation, the informational distance, that we believe may be of significance in other contexts as well.

35 pages. Uses IEEEtran.cls, IEEEbib.bst. Submitted to IEEE Transactions on Information Theory. Strengthens results in quant-ph/0005106, quant-ph/0004100 and an earlier version presented in STOC 2001

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