Toward Quantum Combinatorial Games
نویسندگان
چکیده
In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff [2006]. A Combinatorial Game is a two-player game with no chance and no hidden information, such as Go or Chess. In this paper, we consider the possibility of playing superpositions of moves in such games. We propose different rulesets depending on when superposed moves should be played, and prove that all these rulesets may lead similar games to different outcomes. We then consider Quantum variations of the game of Nim. We conclude with some discussion on the relative interest of the different rulesets.
منابع مشابه
Conditional combinatorial games and their application to analyzing capturing races in Go
Conditional combinatorial games (CCG) are a new tool developed for describing loosely coupled games. The definition of CCG is based on the one for classical independent combinatorial games. However, play in a CCG depends on its global context: certain moves are legal only if a nonlocal context condition is currently true. Compared with independent combinatorial games, CCG only allow some weaker...
متن کاملScaling, Renormalization, and Universality in Combinatorial Games: The Geometry of Chomp
We develop a new approach to combinatorial games (e.g., chess, Go, checkers, Chomp, Nim) that unveils connections between such games and nonlinear phenomena commonly seen in nature: scaling behaviors, complex dynamics and chaos, growth and aggregation processes. Using the game of Chomp (as well as variants of the game of Nim) as prototypes, we discover that the game possesses an underlying geom...
متن کاملParallel Repetition via Fortification: Analytic View and the Quantum Case
In a recent work, Moshkovitz [FOCS ’14] presented a transformation on two-player games called “fortification”, and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz’s fortification framework, which was originally cast in combinatorial terms. This reformulation a...
متن کاملContextuality in Multipartite Pseudo-Telepathy Graph Games
Analyzing pseudo-telepathy graph games, we propose a way to build contextuality scenarios exhibiting the quantum supremacy using graph states. We consider the combinatorial structures generating equivalent scenarios. We investigate which scenarios are more multipartite and show that there exist graphs generating scenarios with a linear multipartiteness width.
متن کاملOn deciding the existence of perfect entangled strategies for nonlocal games
First, we consider the problem of deciding whether a nonlocal game admits a perfect finite dimensional entangled strategy that uses projective measurements on a maximally entangled shared state. Via a polynomial-time Karp reduction, we show that independent set games are the hardest instances of this problem. Secondly, we show that if every independent set game whose entangled value is equal to...
متن کامل