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Quantum-Optical set-up for the Monty Hall problem and a secure communication protocol

Luis Fernando Quezada, A. Martín-Ruiz, Alejandro Frank, Eduardo Nahmad-Achar

Published Aug 15, 2019• 0 citations
OpenAlex

Abstract

A quantization scheme for the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied from a frequentist perspective by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. A potential application to secure communications of this quantization scheme and its results is also briefly discussed.

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A quantization scheme for the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied from a frequentist perspective by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. A potential application to secure communications of this quantization scheme and its results is also briefly discussed.
Abstract A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined by considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. We also discuss the influence of noise on the game outcome when the parties play through a noisy quantum channel. The experimental set-up can be used to quickly verify the counter-intuitive result of the Monty Hall problem, adding pedagogic value to the proposal.
Abstract In this work, the authors propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free and not fixed on its regular values. The developed quantum scheme is then used to study the expected payoff of the player, using both a separable and an entangled initial‐state. In the two cases, the classical mixed‐strategy payoff is recovered under certain conditions. Lastly, the authors extend the quantum scheme to include multiple independent players, and use this extension to sketch two possible application of the game mechanics to quantum networks, specifically, two validated, multi‐party, key‐distribution quantum protocols.
A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than that obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qutrits of the two players, it is advantageous for one player to have access to a quantum strategy while the other does not. Where both players have access to quantum strategies there is no Nash equilibrium in pure strategies, however, there is a Nash equilibrium in quantum mixed strategies that gives the same average payoff as the classical game.
We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.
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 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, 3-qubit symmetric W state, 3-qubit X state, and 5-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.
We propose a framework for quantizing randomized quantum games in which entanglement is examined as a tunable fairness resource without relying on fine-tuned strategy parameters. As a case study of the Monty Hall problem, we show that initial entanglement between host and player registers neutralizes classical asymmetry at the distribution level, driving win-probability distributions under different strategic conditions to converge. Implemented on IBM’s Eagle processors via four-qubit encodings, our experiments span a continuum of entanglement strengths and employ extensive randomized trials over broad strategy ensembles. Although the mean no-switch probability remains fixed at its classical value, stronger entanglement progressively suppresses distributional signatures of asymmetric play, yielding increasingly uniform outcome statistics across adversarial conditions. Within the pure-state setting studied here, these findings provide evidence for an experimentally accessible route to quantify entanglement-enabled fairness in quantum games and suggest relevance to quantum information settings involving strategic decision-making under asymmetry.