Timeline for Quantum channels as categories: question 1.
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Jun 14, 2010 at 16:41 | answer | added | Greg Kuperberg | timeline score: 8 | |
| Jun 14, 2010 at 16:05 | answer | added | supercooldave | timeline score: 0 | |
| Feb 24, 2010 at 6:51 | history | edited | Kim Morrison | CC BY-SA 2.5 |
deleted 222 characters in body
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| Feb 1, 2010 at 17:56 | vote | accept | Ian Durham | ||
| Feb 1, 2010 at 1:29 | answer | added | joshuahhh | timeline score: 7 | |
| Feb 1, 2010 at 0:01 | history | edited | Ian Durham | CC BY-SA 2.5 |
Added a note about Kraus operators.
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| Jan 31, 2010 at 22:13 | answer | added | Yemon Choi | timeline score: 5 | |
| Jan 31, 2010 at 21:45 | comment | added | Ian Durham |
Yes. I reread your question a couple of times and I'm pretty sure that the answer is yes. Just to clarify, $\mathcal{C}$ has a specific "dimension" (I use this since it's a relic of the idea of talking about a $d$-dimensional Hilbert space - originally I was using Hilbert spaces as the objects, but then generalized to C$^{*}$-algebra. I felt it better covered any possible classical inputs if that makes sense.
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| Jan 31, 2010 at 21:21 | comment | added | Yemon Choi | I might be misunderstanding your terminology: according to the Wikipedia article, a quantum channel is a completely-positive trace-preserving map on an ambient finite-dimensional C*-algebra ${\mathcal C}$. (I don't think calling $d$ the dimension of the $C^*$-algebra is standard, but could be wrong here.) Now it seems that what you are asking is whether the set of all such channels forms the set of arrows for a 1-object category whose object is ${\mathcal C}$. Is that right? | |
| Jan 31, 2010 at 21:09 | history | asked | Ian Durham | CC BY-SA 2.5 |