Secret Information Sharing using Multipartite Entanglement in Monty Hall Game

Abstract

Quantum computing has emerged as a useful resource for winning random games. Monty Hall problem is one such game, where the powers of quantum mechanics can be utilized for winning the prize. Our paper depicts this problem as a two-player game, where the two players, i.e., the host and the participant share an entangled quantum state. The entangled state is closely knit with the position of the prize containing door, and the decision of the player i.e., either switch or stay from his initial choice of door. The two players are part of one team as they share a quantum communication channel among them by sharing the entangled state as a quantum resource. This enables them to share secret information about the position of the price as well as the strategy to opt for winning the game. The article shows a unique way of utilizing three different type of entangled states, three-qubit symmetric W state, three-qubit \(\chi \) state, and five-qubit highly entangled Brown state. Further, the effectiveness of each quantum state as a source of communication in disguise is also compared. All the entangled states under study assure winning the price by the participant. However, each quantum state has different entanglement degree and offer varied merits as per the game setting.