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arXiv:quant-ph/0206167

Optimal Guessing Strategies in a Quantum Card Game

Chih‐Lung Chou, Li‐Yi Hsu

Published Jun 24, 2002• 0 citations
arXivHTMLPDF

Abstract

Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know better than Alice does on guessing Alice's card, no matter what Bob chooses to measure his two cards collectively or separately. We also find that Bob's best strategy for guessing Alice's card is to measure his two cards collectively.

DOI
10.48550/arxiv.quant-ph/0206167

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Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know better than Alice does on guessing Alice's card, no matter what Bob chooses to measure his two cards collectively or separately. We also find that Bob's best strategy for guessing Alice's card is to measure his two cards collectively.
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We present a guessing to be called secret-bit guessing game, where a player (say, Bob) guesses two secret bits enveloped by another player (say, Alice) based on a legitimate strategy. Here we introduce a notion of supplementary information, under the name of hint, available for Bob to guess the secret bits. In such setting, we investigate an intriguing question: What happens if the physical elements to realize Bob's strategy are quantum? On the basis of the analysis of payoff function, we here offer a new scenario, namely, of allowing Bob to make better use of a given hint with the quantum elements beyond their classical counterparts. We argue that this quantum advantage is possible due to the ability of the quantum elements to use the quality of a given hint, as well as its amount, faithfully dealing with the nature of quantum superposition.
Abstract In a variant of communication tasks, players cooperate in choosing their local strategies to compute a given task later, working separately. Utilizing quantum bits for communication and sharing entanglement between parties is a recognized method to enhance performance in these situations. In this work, we introduce the game for which three parties, Alice, Bob and Charlie, would like to discover the hidden order in which they make the moves. We show the advantage of quantum strategies that use shared entanglement and local operations over classical setups for discriminating operations’ composition order. The role of quantum resources improving the probability of successful discrimination is also investigated. Our research provides a basis for examining computational model featuring a specific gate set while examining the diverse operations achievable through permutations of its elements.
Newcomb’s problem is a game between two players, one of who has an ability to predict the future: let Bob have an ability to predict Alice’s will. Now, Bob prepares two boxes, Box1 and Box2, and Alice can select either Box2 or both boxes. Box1 contains $1. Box2 contains $1,000 only if Alice selects only Box2; otherwise Box2 is empty($0). Which is better for Alice? Since Alice cannot decide which one is better in general, this problem is called Newcomb’s paradox. In this paper, we propose quantum strategies for this paradox by Bob having quantum ability. Many other results including quantum strategies put emphasis on finding out equilibrium points. On the other hand, our results put emphasis on whether a player can predict another player’s will. Then, we show some positive solutions for this problem.