Consumable data via quantum communication

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 x and Bob holds m inputs y 1 , … , y m . They want to compute m instances of a bipartite relation R ( · , · ) on every pair ( x , y 1 ) , … , ( x , y m ) . We call this the asymmetric direct sum question for one-way communication. We give examples where the quantum communication complexity of such problems scales polynomially with m , while the classical communication complexity depends at most logarithmically on m . Thus, for such problems, data behaves like a consumable resource that is effectively destroyed upon use when the owner stores and transmits it as quantum states, but not when transmitted classically. We show an application to a strategic data-selling game, and discuss other potential economic implications.