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Consumable Data via Quantum Communication

Main:14 Pages
Bibliography:6 Pages
1 Tables
Appendix:4 Pages
Abstract

Classical data can be copied and re-used for computation, with adverse consequences economically and in terms of data privacy. Motivated by this, we formulate problems in one-way communication complexity where Alice holds some data and Bob holds mm inputs, and he wants to compute mm instances of a bipartite relation on Alice's data and each of his inputs. We call this the asymmetric direct sum question for one-way communication. We give a number of examples where the quantum communication complexity of such problems scales polynomially with mm, while the classical communication complexity depends at most logarithmically on mm.

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