Toward Quantum Combinatorial Games presents the definition of a "quantum game", allowing a superposition of moves rather than a single classical move. This leaves me wondering: Since surreal numbers are a certain class of games, is there a similar class of "quantum surreal numbers" formed from quantum games, but richer than the surreals? What properties or structure do they have?
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1$\begingroup$ surreal numbers are special cases of combinatorial games, so if you can define quantum combinatorial games (I assume as superpositions of classical games) you also know what a quantum surreal is: the superposition of two games which happen to be surreal numbers $\endgroup$– Mirco A. MannucciCommented Aug 23, 2020 at 11:59
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2$\begingroup$ @MircoA.Mannucci Might be more invloved than that: "numberness" of a quantum game might be a quantity (such as probability, say) rather than a property. $\endgroup$– მამუკა ჯიბლაძეCommented Aug 23, 2020 at 13:14
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$\begingroup$ Mamuka, I see your point: surreal numbers are not simply some special games (essentially the silly ones) but serve as "numbers" to gauge them. Ok, things might be more involved, but why not trying first the simple minded approach I mentioned? Conjecture: my simple quantum surreal work well when a quantum game is not entangled, else you need some more sophisticated weapon... $\endgroup$– Mirco A. MannucciCommented Aug 23, 2020 at 13:25
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$\begingroup$ @Mirco: are we superposing games or moves (or both)? $\endgroup$– QfwfqCommented Aug 23, 2020 at 13:39
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$\begingroup$ @Qfwfq in the above I was simply generalizing to simple-minded superposition of games, but why stopping there? The interesting beasts are games where the moves are superpositions of classical moves. PS Conway would have loved that... $\endgroup$– Mirco A. MannucciCommented Aug 23, 2020 at 13:58
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