Non-locality and Communication Complexity

TL;DR

This paper reviews how quantum mechanics, especially non-locality and entanglement, can dramatically reduce communication complexity in distributed computing tasks, revealing foundational physics insights and practical quantum protocols.

Contribution

It connects non-locality with quantum communication complexity, highlighting how entanglement enables exponential reductions in communication requirements.

Findings

Quantum protocols demonstrate exponential communication savings.

Entanglement cannot replace communication but reduces it significantly.

Links between non-locality and computational advantages are established.

Abstract

Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. We review the area of quantum communication complexity, and show how it connects the foundational physics questions regarding non-locality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on non-locality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics, and could even yield new proposals for experiments that test the foundations of physics.