Simple Information Processing Tasks with Unbounded Quantum Advantage

TL;DR

This paper demonstrates that simple quantum communication tasks can outperform classical systems unboundedly, showing quantum advantage in minimal scenarios and highlighting the resource costs of classical implementations.

Contribution

It constructs tasks where quantum systems outperform classical ones unboundedly, even with shared randomness, emphasizing the resource gap.

Findings

Quantum systems can implement tasks with single qubits that require unbounded classical resources.

Classical implementations need unboundedly larger systems and coordination, even with shared randomness.

Shared randomness is not a free resource for classical implementations of quantum tasks.

Abstract

Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbounded advantage of quantum systems over classical systems. We do this by constructing a family of operationally meaningful communication tasks each of which on one hand can be implemented by using just a single qubit but which on the other hand require unboundedly larger classical system for classical implementation. Furthemore, we show that even though with the additional resource of shared randomness the proposed communication tasks can be implemented by both quantum and classical systems of the same size, the number of coordinated actions needed for the classical implementation also grows unboundedly. In particular, no finite storage can be used to store all the coordinated actions needed to implement all the possible quantum communication tasks with classical systems. As a consequence, shared randomness cannot be viewed as a free resource.