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1. • CommentRowNumber1.
   • CommentAuthorTobyBartels
   • CommentTimeOct 14th 2014
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI put some simple examples of spaces of states at [[state]], up to the qubit (which is shaped like an American football, who knew?).

   I put some simple examples of spaces of states at state, up to the qubit (which is shaped like an American football, who knew?).

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 14th 2014
   • (edited Oct 14th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. By the way, we have an entry _[[qbit]]_. I made _[[qubit]]_ redirect to it now. Should we right away make _[[line segment]]_ redirect to something, too? Maybe to _[[interval]]_? (If we don't un-gray that link right now, then we will forget about it and it will stay gray forever.)

   Thanks.

   By the way, we have an entry qbit. I made qubit redirect to it now.

   Should we right away make line segment redirect to something, too? Maybe to interval? (If we don’t un-gray that link right now, then we will forget about it and it will stay gray forever.)

3. • CommentRowNumber3.
   • CommentAuthorRodMcGuire
   • CommentTimeOct 15th 2014
   • PermaLink
   Author: RodMcGuire
   Format: MarkdownItex> which is shaped like an American football Strangely enough the American "pig skin" (actually pig bladder) is the surface of revolution of a fish bladder ([vesica piscis](http://en.wikipedia.org/wiki/Vesica_piscis)).

   which is shaped like an American football

   Strangely enough the American “pig skin” (actually pig bladder) is the surface of revolution of a fish bladder (vesica piscis).

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeOct 17th 2014
   • (edited Oct 17th 2014)
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexThe length ratio doesn\'t match this shape. (Although I think that only the convex-linear structure is relevant.) ETA: Actually, there *is* a metric structure, since the states sit within a Banach space (the predual of the algebra of observables). But this is a *different* metric structure. Even for the classical bit, although I parametrized with a variable running from $0$ to $1$, its length is actually $2$. (It runs from $(0,1)$ to $(1,0)$ in $l^1(2)$.)

   The length ratio doesn't match this shape. (Although I think that only the convex-linear structure is relevant.)

   ETA: Actually, there is a metric structure, since the states sit within a Banach space (the predual of the algebra of observables). But this is a different metric structure. Even for the classical bit, although I parametrized with a variable running from $0$ to $1$, its length is actually $2$. (It runs from $(0,1)$ to $(1,0)$ in $l^1(2)$.)

5. • CommentRowNumber5.
   • CommentAuthorTobyBartels
   • CommentTimeOct 17th 2014
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItex@ Urs: Well, [[interval]] claims to be about the order-theoretic concept. It links to [[interval object]] for the homotopy-theoretic interval, although it mentions it later just about the geometric interval. It would make more sense to me if that too had its own page, which would arguably be [[line segment]]. (If we leave it grey, it won\'t stay that way forever! I fill in my grey links from time to time.)

   @ Urs: Well, interval claims to be about the order-theoretic concept. It links to interval object for the homotopy-theoretic interval, although it mentions it later just about the geometric interval. It would make more sense to me if that too had its own page, which would arguably be line segment.

   (If we leave it grey, it won't stay that way forever! I fill in my grey links from time to time.)

6. • CommentRowNumber6.
   • CommentAuthorTobyBartels
   • CommentTimeDec 11th 2022
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexOn further reflection, this incorrect metric structure is very misleading! The lemon/football shape has two distinguished points, the vertices, which correspond to the pure states $\lvert0\rangle$ and $\lvert1\rangle$. But these two states are *not* distinguished, since you could as easily use $\lvert{+}\rangle \coloneqq \sqrt2/2\lvert0\rangle + \sqrt2/2\lvert1\rangle$ and $\lvert{-}\rangle \coloneqq \sqrt2/2\lvert0\rangle - \sqrt2/2\lvert1\rangle$ (or some other combination) instead. The lemon is an artifact of the description using $a$, $b$, and $c$; the actual shape is a ball (the Bloch ball, whose surface is the Bloch sphere). I\'ve edited the page to reflect this, sadly removing all references to sports and fruit. I also added a bit in the intro, where we\'re looking at different kinds of states in physics, about microstates and macrostates. And I even finished the first sentence. But now there are yet more grey links.

   On further reflection, this incorrect metric structure is very misleading! The lemon/football shape has two distinguished points, the vertices, which correspond to the pure states $\lvert0\rangle$ and $\lvert1\rangle$. But these two states are not distinguished, since you could as easily use $\lvert{+}\rangle \coloneqq \sqrt2/2\lvert0\rangle + \sqrt2/2\lvert1\rangle$ and $\lvert{-}\rangle \coloneqq \sqrt2/2\lvert0\rangle - \sqrt2/2\lvert1\rangle$ (or some other combination) instead. The lemon is an artifact of the description using $a$, $b$, and $c$; the actual shape is a ball (the Bloch ball, whose surface is the Bloch sphere). I've edited the page to reflect this, sadly removing all references to sports and fruit.

   I also added a bit in the intro, where we're looking at different kinds of states in physics, about microstates and macrostates. And I even finished the first sentence. But now there are yet more grey links.