Exponential quantum enhancement for distributed addition with local nonlinearity

TL;DR

This paper demonstrates that entanglement-assisted quantum protocols can exponentially reduce the communication required for distributed nonlinear Boolean function computation, specifically in distributed integer addition.

Contribution

It introduces a scheme showing exponential quantum advantage in distributed addition with local nonlinearity, highlighting the power of entanglement in reducing communication complexity.

Findings

Entanglement-assisted protocols require exponentially fewer communication channels.

Quantum methods outperform classical in distributed nonlinear Boolean functions.

Exponential enhancement demonstrated for distributed integer addition.

Abstract

We consider classical and entanglement-assisted versions of a distributed computation scheme that computes nonlinear Boolean functions of a set of input bits supplied by separated parties. Communication between the parties is restricted to take place through a specific apparatus which enforces the constraints that all nonlinear, nonlocal classical logic is performed by a single receiver, and that all communication occurs through a limited number of one-bit channels. In the entanglement-assisted version, the number of channels required to compute a Boolean function of fixed nonlinearity can become exponentially smaller than in the classical version. We demonstrate this exponential enhancement for the problem of distributed integer addition.