Timeline for Looking for an example of an operator that will not converge on maximally mixed state
Current License: CC BY-SA 3.0
4 events
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| Feb 29, 2016 at 11:41 | comment | added | Norbert Schuch | I'm not sure what you mean by the Haar measure for quantum channels, but for any reasonable (i.e., non-delta) measure, I would indeed expect that all channels except a set of measure 0 have a unique fixed point. (A second fixed point corresponds to a second eigenvalue of $\mathcal E$ on the unit circle, which should have probability 0 w.r.t. any smooth measure.) | |
| Feb 29, 2016 at 0:36 | comment | added | XXDD | Thanks so much for showing me the example. A quick question, as you mentioned in your previous response, most of quantum channels will converge to a fixed state, may I guess that such unconverged case is rare (maybe with probability 0 w.r.t. Haar measure)? | |
| Feb 29, 2016 at 0:27 | vote | accept | XXDD | ||
| Feb 28, 2016 at 17:01 | history | answered | Norbert Schuch | CC BY-SA 3.0 |