User talk:Aquohn
I'm curious what you meant with this edit [1] to the POVM article. It is clearly incorrect, as the dimension must increase with the number of outcomes; I couldn't find the assertion in the paper you cited either. Maybe it is just a typo and something similar is true? Tercer (talk) 08:03, 19 April 2022 (UTC)
Oh, yes, that's a typo. It should be nk not kd_A. The paper mentions that, when the dilated space A' is of dimension nk (using our notation), the POVMs from sampling it are of rank k with probability 1. I think, strictly speaking, some more work is needed to show that it is sufficient for the dilation, but I'm quite sure it's true. Aquohn (talk) 08:23, 19 April 2022 (UTC)
- Ah, yes, then I totally believe it is true. Nevertheless, we can't add that to the article if the paper doesn't state it explicitly. The result by Peres it mentions is clearly valid only for rank-1 POVMs, we should correct that. Tercer (talk) 09:24, 19 April 2022 (UTC)
- Yes, that was my initial motivation for editing it: the original claim was misleading, and I wanted to replace it with the correct and more general statement. I don't think I've seen it stated explicitly, although it's not difficult to show. Thanks for catching my mistake though! Aquohn (talk) 05:26, 21 April 2022 (UTC)