Maximum Separation of Quantum Communication Complexity With and Without Shared Entanglement

TL;DR

This paper demonstrates the largest known separation in quantum communication complexity between models with and without shared entanglement, using relation problems and parallel repetition of non-local games.

Contribution

It establishes the first lower bound on quantum communication complexity without shared entanglement for problems solvable with entanglement, refuting a quantum version of Newman's theorem.

Findings

No communication is needed with entanglement-assisted quantum models.

Omega(n) qubits are required without shared entanglement.

First lower bound established for quantum models without entanglement.

Abstract

We present relation problems whose input size is $n$ such that they can be solved with no communication for entanglement-assisted quantum communication models, but require $\Omega(n)$ qubit communication for $2$-way quantum communication models without prior shared entanglement. This is the maximum separation of quantum communication complexity with and without shared entanglement. To our knowledge, our result even shows the first lower bound on quantum communication complexity without shared entanglement when the upper bound of entanglement-assisted quantum communication models is zero. Our result refutes a quantum analog of Newman's theorem. The problem we consider is parallel repetition of any non-local game which has a perfect quantum strategy and no perfect classical strategy, and for which a parallel repetition theorem holds with exponential decay.