Timeline for Retractions for completely positive unital maps, with particularly nice norms
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 13, 2017 at 14:43 | history | bounty ended | Niel de Beaudrap | ||
| Nov 8, 2017 at 17:50 | vote | accept | Niel de Beaudrap | ||
| Nov 8, 2017 at 11:07 | vote | accept | Niel de Beaudrap | ||
| Nov 8, 2017 at 11:27 | |||||
| Nov 7, 2017 at 19:43 | comment | added | Chris Ramsey | @NieldeBeaudrap Thanks for the original question, I hadn't ever thought about the inverses of ucp maps before. No, I don't have an argument that this $S$ is achieving the cb norm, but it seems highly likely that it does given that it is a riff on the transpose. | |
| Nov 7, 2017 at 19:19 | comment | added | Niel de Beaudrap | This is a nice example: $\Psi$ also happens to be trace-preserving, and in particular a convex combination of isometries. This hints how to produce other counterexamples (and is another proof that $\Psi$ is CP). The operator norm of $\Phi$ turns out to be precisely $5$, with $\lVert \Phi(Z) \rVert = 5$ for $Z = \mathrm{diag}(1,-1)$, whereas you've provided a value of $S$ for which one can show $\lVert \Phi^{(2)}(S) \rVert = 5.5$. Out of curiosity, do you happen to have an argument for whether $S$ achieves the maximum in this case? | |
| S Nov 6, 2017 at 19:17 | history | suggested | Niel de Beaudrap | CC BY-SA 3.0 |
fixed another apparent typo
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| Nov 6, 2017 at 19:11 | review | Suggested edits | |||
| S Nov 6, 2017 at 19:17 | |||||
| S Nov 6, 2017 at 19:08 | history | suggested | Niel de Beaudrap | CC BY-SA 3.0 |
fixed apparent typo and made minor change to formatting
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| Nov 6, 2017 at 19:07 | review | Suggested edits | |||
| S Nov 6, 2017 at 19:08 | |||||
| Nov 5, 2017 at 13:31 | history | edited | Chris Ramsey | CC BY-SA 3.0 |
Clarified some details of my answer
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| Nov 4, 2017 at 1:21 | history | answered | Chris Ramsey | CC BY-SA 3.0 |