Analysing the role of entanglement in the three-qubit Vaidman's game

TL;DR

This paper investigates how different levels of entanglement in three-qubit states influence the success of quantum strategies in Vaidman's game, revealing conditions where quantum advantages are guaranteed and proposing a new game involving an entangled rule maker.

Contribution

It identifies conditions under which quantum strategies outperform classical ones in Vaidman's game and introduces a novel game with an entangled rule maker for secret sharing.

Findings

Partially entangled states may not always enhance winning probability.

Certain W states guarantee success regardless of entanglement degree.

A new Vaidman-type game with an entangled rule maker is proposed.

Abstract

We analyse the role of degree of entanglement for Vaidman's game in a setting where the players share a set of partially entangled three-qubit states. Our results show that the entangled states combined with quantum strategies may not be always helpful in winning a game as opposed to the classical strategies. We further find the conditions under which quantum strategies are always helpful in achieving higher winning probability in the game in comparison to classical strategies. Moreover, we show that a special class of W states can always be used to win the game using quantum strategies irrespective of the degree of entanglement between the three qubits. Our analysis also helps us in comparing the Vaidman's game with the secret sharing protocol. Furthermore, we propose a new Vaidman-type game where the rule maker itself is entangled with the other two players and acts as a facilitator to share a secret key with the two players.