When we talk about a two-state quantum system being a two-dimensional complex Hilbert space are we implicitly considering the "existence of time"? Why is all this additional structure (of a two-dimensional complex Hilbert space) necessary if, even with a full quantum mechanical perspective, asking a yes-no question yields either yes or no as the answer? I know there are going to be(adsbygoogle = window.adsbygoogle || []).push({}); timeswhere the answer will be in a superposition of yes and no, but so far nothing has been said abouttimeso that point is moot. Is it that the yes-no question is being combined with the question "what time is it?" and thenthatresults in a two-dimensional complex Hilbert space? In this case, which mathematical structures represent the "two-state system" and time so we can take their tensor products and get the Hilbert space?

Also, are all the properties of a Hilbert space necessary for the two-state system with time? What is the quantum mechanical interpretation of the addition of two vectors?

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# Why two-state system = two-dimensional Hilbert space?

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