#### Data as a Consumable Resource

**ICML 2024** Workshop on Agentic Markets

## Abstract

We formulate asymmetric direct sum problems in one-way communication complexity.
In such problems, Alice receives one input and Bob receives m inputs. Bob's goal is to compute relations on Alice's input and each one of his inputs.
We give a number of examples where the quantum communication complexity of these problems scales polynomially with m, while the classical communication complexity does not.
This is motivated by the observation that data is relevant as an economic resource, especially with the prevalence of data-hungry parameterized models.
But classically, data can be copied at essentially no cost without leaving a record, which is an issue for the data owner.
On the other hand, our results are interpreted to say that for certain problems data behaves like a consumable resource when the owner has the ability to store and transmit data encoded in quantum states.
This has potential applications to the design of data markets and competitive games involving data.