Timeline for Eigenvalues of density operator under quantum channel
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2015 at 15:28 | comment | added | Girish Kulkarni | @Martin Majorization was just the thing I needed. Also, the reference by Nielsen that you provided is very useful indeed. Thanks a lot for your spot-on answer. | |
| Sep 15, 2015 at 15:25 | vote | accept | Girish Kulkarni | ||
| Sep 14, 2015 at 17:03 | comment | added | Martin | @Girish: Sure, if any questions remain, please ask away! If you at some point need to go a bit deeper into majorization, there is a book by Michael Nielsen about it and I can also suggest the beautiful book "Matrix Analysis" by Bhatia. | |
| Sep 14, 2015 at 16:25 | comment | added | Girish Kulkarni | @Martin Thank you for your detailed and helpful answer. I'll need to familiarize with the idea of majorization and work out the details for myself. I will get back to you on this thread. | |
| Sep 14, 2015 at 13:34 | history | edited | Martin | CC BY-SA 3.0 |
added material according to changed question.
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| Sep 14, 2015 at 11:17 | comment | added | Emilio Pisanty | @Girish Well, it can - that's a 'scrap and re-prepare' map. Whether you can set up a careful quantification of outside interference that that map runs foul of is another question. | |
| Sep 14, 2015 at 11:17 | comment | added | Norbert Schuch | @Girish Martin's map is perfectly CPTP. There is no statement saying that the entropy of a system coupled to a bath has to increase. (Just consider a cold bath and an initially warm system!) | |
| Sep 14, 2015 at 11:08 | comment | added | Girish Kulkarni | @Emilio Ok thanks. I have edited the problem to include more details. Also, I am not really sure about Martin's map since it seems to suggest that any dxd quantum state can evolve into any nxn quantum state. | |
| Sep 14, 2015 at 10:58 | comment | added | Emilio Pisanty | @Girish So you're saying that Martin's map is not CP? (Could be, it's been a while since I've dealt with those.) In any case, specify clearly in your question which class of maps you're dealing with. Provide a well-posed mathematical problem, with the specifications up front and well labeled. | |
| Sep 14, 2015 at 10:50 | comment | added | Emilio Pisanty | @Girish You should make those restrictions clear in your question. | |
| Sep 14, 2015 at 10:45 | comment | added | Girish Kulkarni | Thank you for your reply. I am interested in the physical evolution of density operators which have the constraint that the Von-Neumann entropy cannot decrease. It is not obvious to me if the above map you mention indeed respects this constraint. | |
| Sep 14, 2015 at 10:32 | history | answered | Martin | CC BY-SA 3.0 |