Timeline for Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2011 at 2:17 | vote | accept | Jess Riedel | ||
| May 17, 2011 at 2:17 | comment | added | Jess Riedel | This answer seems to be best currently available, so I'm accepting it. If I make any progress, or find more comprehensive info elsewhere, I'll post it as a separate answer. | |
| May 17, 2011 at 2:15 | comment | added | Jess Riedel | I don't think your argument for the Schmidt decomposition minimizing entropy goes through because I am considering the set of all possible orthonomal bases of product states, not just those canonically constructed from local bases of the subsystems. Nonetheless, I have proven the claim is true by constructing explicitly a sequence of decomps, from an arbitrary product-state decomp to the Schmidt decomp, which are ordered by the majorization partial order. This proves the Schmidt decomposition minimizes all functions F[{p_i}] = sum_i f(p_i) of the spectrum, f(p) concave, not just entropy. | |
| May 9, 2011 at 17:21 | history | answered | Sebastian Meznaric | CC BY-SA 3.0 |