{"title":"量子塔普西罗--受希腊传统掷硬币游戏 \"塔普西罗 \"启发的量子游戏","authors":"Kalliopi Kastampolidou, T. Andronikos","doi":"10.3390/g14060072","DOIUrl":null,"url":null,"abstract":"This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the classical game, both players have 14 probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding Ry rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action.","PeriodicalId":35065,"journal":{"name":"Games","volume":"47 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum Tapsilou—A Quantum Game Inspired by the Traditional Greek Coin Tossing Game Tapsilou\",\"authors\":\"Kalliopi Kastampolidou, T. Andronikos\",\"doi\":\"10.3390/g14060072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the classical game, both players have 14 probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding Ry rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action.\",\"PeriodicalId\":35065,\"journal\":{\"name\":\"Games\",\"volume\":\"47 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Games\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/g14060072\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/g14060072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
摘要
本文介绍了一种名为 "量子塔普西罗"(Quantum Tapsilou)的新量子游戏,其灵感来自希腊传统的经典掷硬币游戏 "塔普西罗"(tapsilou)。尽管新量子游戏的复杂性和范围都有所增加,但它保留了传统游戏最重要的特点。在古典游戏中,双方都有 14 的概率获胜。量子版保留了这一特点,即双方都有相同的获胜概率,只是现在这种概率变化很大,而且取决于之前的棋步和选择。量子塔普西罗的两个最重要的新颖之处可归因于它通过使用旋转门而不是哈达玛门实现了纠缠,从而产生了具有不等概率振幅的类似贝尔的状态,以及组的整体使用。在量子塔普西罗棋中,棋手双方都同意在某个足够大的 n 中选择一个特定的 n 阶循环旋转群。更具体地说,双方都将从这个组中选择旋转,使用相应的 Ry 旋转门来实现他们的行动。在量子塔普西罗棋局中,双方获胜的可能性相同。这一事实与之前文献中的一个结果相一致,即量子博弈中,如果双方都从同一组中选择棋子,那么双方都有可能选择与对方的棋子相抵消的棋子,从而表现出完美的对称性。
Quantum Tapsilou—A Quantum Game Inspired by the Traditional Greek Coin Tossing Game Tapsilou
This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the classical game, both players have 14 probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding Ry rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action.
GamesDecision Sciences-Statistics, Probability and Uncertainty
CiteScore
1.60
自引率
11.10%
发文量
65
审稿时长
11 weeks
期刊介绍:
Games (ISSN 2073-4336) is an international, peer-reviewed, quick-refereeing open access journal (free for readers), which provides an advanced forum for studies related to strategic interaction, game theory and its applications, and decision making. The aim is to provide an interdisciplinary forum for all behavioral sciences and related fields, including economics, psychology, political science, mathematics, computer science, and biology (including animal behavior). To guarantee a rapid refereeing and editorial process, Games follows standard publication practices in the natural sciences.