Consumable Data via Quantum Communication

TL;DR

This paper explores how quantum communication can make data effectively consumable and non-reusable, contrasting it with classical methods, with implications for data privacy and economic models.

Contribution

It introduces the asymmetric direct sum problem in quantum communication, demonstrating polynomial quantum complexity versus logarithmic classical complexity for certain data tasks.

Findings

Quantum communication complexity scales polynomially with data reuse

Classical complexity depends logarithmically on data reuse

Quantum data transmission can destroy data, unlike classical methods

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 $x$ and Bob holds $m$ inputs $y_1,... , y_m$. They want to compute $m$ instances of a bipartite relation $R$ on every pair $(x, y_1),\ldots, (x, y_m)$. 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 $m$, 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.