The Impossibility of Pseudo-Telepathy Without Quantum Entanglement

TL;DR

This paper proves that quantum entanglement enables perfect success in a communication-free distributed task, whereas classical resources cannot achieve the same, highlighting the unique power of quantum entanglement.

Contribution

It demonstrates the impossibility of pseudo-telepathy without quantum entanglement for a specific game, completing the analysis of such tasks.

Findings

Quantum entanglement allows perfect success without communication.

Classical resources cannot achieve the task with certainty, regardless of resources.

The result emphasizes the non-classical nature of quantum correlations.

Abstract

Imagine that Alice and Bob, unable to communicate, are both given a 16-bit string such that the strings are either equal, or they differ in exactly 8 positions. Both parties are then supposed to output a 4-bit string in such a way that these short strings are equal if and only if the original longer strings given to them were equal as well. It is known that this task can be fulfilled without failure and without communication if Alice and Bob share 4 maximally entangled quantum bits. We show that, on the other hand, they CANNOT win the same game with certainty if they only share classical bits, even if it is an unlimited number. This means that for fulfilling this particular distributed task, quantum entanglement can completely replace communication. This phenomenon has been called pseudo-telepathy. The results of this paper complete the analysis of the first proposed game of this type between two players.