User sep332 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T13:52:29Z http://mathoverflow.net/feeds/user/2576 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/13396/are-the-gell-mann-matrices-extremal-when-used-as-kraus-operators-for-a-quantum-ch Are the Gell-Mann matrices extremal when used as Kraus operators for a quantum channel? sep332 2010-01-29T18:39:53Z 2012-05-31T13:30:06Z <p>Landau and Streater proved that a set of Kraus operators, Ai, is extremal if and only if the set</p> <p>$\{A_{k}^{\dagger}A_{l}\}_{k,l \ldots N}$ </p> <p>are linearly independent. I have seen very convincing arguments both for and against. You can even see two PDFs of Mathematica notebooks "proving" <em>both</em> answers here: <a href="http://quantummoxie.wordpress.com/2010/01/28/a-quirky-mathematical-problem-in-need-of-explanation/" rel="nofollow">http://quantummoxie.wordpress.com/2010/01/28/a-quirky-mathematical-problem-in-need-of-explanation/</a></p> <p>What is missing from these proofs?</p> http://mathoverflow.net/questions/18375/is-there-any-finitely-long-sequence-of-digits-which-is-not-found-in-the-digits-of Is there any finitely-long sequence of digits which is not found in the digits of pi? sep332 2010-03-16T14:02:52Z 2010-11-05T07:09:22Z <p>I know it's likely that, given a finite sequence of digits, one can find that sequence in the digits of pi, but is there a proof that this is possible for all finite sequences? Or is it just very probable?</p> http://mathoverflow.net/questions/13396/are-the-gell-mann-matrices-extremal-when-used-as-kraus-operators-for-a-quantum-ch Comment by sep332 sep332 2010-01-29T19:15:28Z 2010-01-29T19:15:28Z @Jon Thanks for the LaTeX hint and the Streater correction. I will try to rephrase the question so that it makes more sense.