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- W4287201098 abstract "This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and also its possible extensions. We show that the PQ penny flip game can be associated with the dihedral group $D_{8}$. We prove that within $D_{8}$ there exist precisely two classes of winning strategies for Q. We establish that there are precisely two different sequences of states that can guaranteed Q's win with probability $1.0$. We also show that the game can be played in the all dihedral groups $D_{8 n}$, $n geq 1$, with any significant change. We examine what happens when Q can draw his moves from the entire $U(2)$ and we conclude that again, there are exactly two classes of winning strategies for Q, each class containing now an infinite number of equivalent strategies, but all of them send the coin through the same sequence of states as before. Finally, we consider general extensions of the game with the quantum player having $U(2)$ at his disposal. We prove that for Q to surely win against Picard, he must make both the first and the last move." @default.
- W4287201098 created "2022-07-25" @default.
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- W4287201098 date "2021-04-24" @default.
- W4287201098 modified "2023-09-29" @default.
- W4287201098 title "The connection between the $PQ$ penny flip game and the dihedral groups" @default.
- W4287201098 doi "https://doi.org/10.48550/arxiv.2104.12043" @default.
- W4287201098 hasPublicationYear "2021" @default.
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