Abd El-Hakeem E. H. Abd El-Naby, Heba A. Elrayes, Ahmed M. K. Tarabia, Ahmed S. Elgazzar
{"title":"任意最大纠缠量子囚徒困境","authors":"Abd El-Hakeem E. H. Abd El-Naby, Heba A. Elrayes, Ahmed M. K. Tarabia, Ahmed S. Elgazzar","doi":"10.1515/zna-2023-0242","DOIUrl":null,"url":null,"abstract":"The maximally entangled (ME) Eisert–Wilkens–Lewenstein (EWL) quantization scheme efficiently solves the classical prisoner’s dilemma (PD). Despite the intensive research on the EWL scheme, little is known about the role of the arbiter in controlling the scheme properties. We redefine the EWL scheme by introducing an arbitrary phase shift into the ME initial state. Four basic initial states were analyzed in this study. It is found that the arbiter completely controls the characteristics of the arbitrary ME quantum PD. The arbiter can adjust the ME initial state to obtain an efficient symmetric Nash equilibrium. In contrast, the arbiter can nullify the quantization advantages. Moreover, it can preserve/violate the symmetry of the game or even turn it into a potential game.","PeriodicalId":23871,"journal":{"name":"Zeitschrift für Naturforschung A","volume":"57 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Arbitrary maximally entangled quantum prisoner’s dilemma\",\"authors\":\"Abd El-Hakeem E. H. Abd El-Naby, Heba A. Elrayes, Ahmed M. K. Tarabia, Ahmed S. Elgazzar\",\"doi\":\"10.1515/zna-2023-0242\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The maximally entangled (ME) Eisert–Wilkens–Lewenstein (EWL) quantization scheme efficiently solves the classical prisoner’s dilemma (PD). Despite the intensive research on the EWL scheme, little is known about the role of the arbiter in controlling the scheme properties. We redefine the EWL scheme by introducing an arbitrary phase shift into the ME initial state. Four basic initial states were analyzed in this study. It is found that the arbiter completely controls the characteristics of the arbitrary ME quantum PD. The arbiter can adjust the ME initial state to obtain an efficient symmetric Nash equilibrium. In contrast, the arbiter can nullify the quantization advantages. Moreover, it can preserve/violate the symmetry of the game or even turn it into a potential game.\",\"PeriodicalId\":23871,\"journal\":{\"name\":\"Zeitschrift für Naturforschung A\",\"volume\":\"57 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift für Naturforschung A\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/zna-2023-0242\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für Naturforschung A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/zna-2023-0242","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The maximally entangled (ME) Eisert–Wilkens–Lewenstein (EWL) quantization scheme efficiently solves the classical prisoner’s dilemma (PD). Despite the intensive research on the EWL scheme, little is known about the role of the arbiter in controlling the scheme properties. We redefine the EWL scheme by introducing an arbitrary phase shift into the ME initial state. Four basic initial states were analyzed in this study. It is found that the arbiter completely controls the characteristics of the arbitrary ME quantum PD. The arbiter can adjust the ME initial state to obtain an efficient symmetric Nash equilibrium. In contrast, the arbiter can nullify the quantization advantages. Moreover, it can preserve/violate the symmetry of the game or even turn it into a potential game.