Analysing the efficiency of partially entangled states in Vaidman's-type games and its applications in Quantum Secret Sharing

TL;DR

This paper investigates how the degree of entanglement affects the success of quantum strategies in Vaidman's game and introduces a new game involving an entangled rule maker for quantum secret sharing, including analysis under noise.

Contribution

It analyzes the role of partial entanglement in Vaidman's game, identifies conditions where quantum strategies outperform classical ones, and proposes a novel game with an entangled rule maker for secure quantum communication.

Findings

Partially entangled states can sometimes be less effective than classical strategies.

Certain W states guarantee winning with quantum strategies regardless of entanglement degree.

The new game enables secret sharing with an entangled rule maker, even in noisy environments.

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. For practical purposes, the analysis is extended to study the proposed game under noisy conditions. In addition, the results obtained here are also generalized for multi-qubit games.