Undergrad Can POVM measurements be explained by projective measurements?

[Demystifier]

where?

Eq. (18) and the text before it. More details in the link in post #24.

 

[A. Neumaier]

Eq. (18) and the text before it. More details in the link in post #24.

This is not a construction but a sketchy outline of a program that to make it work one would have to justify by a serious derivation.

Instead you make strong assumptions about arbitrary measurements that go far beyond what has been demonstrated in the literature (where always a nondemolition assumption was involved to get decoherence). I had criticised your approach in detail in that thread. I reread the whole thread and still think my criticism is fully valid and that you give nothing but empty phrases and expressions of hope asserted as truth.

Moreover, POVMs appear nowhere - your argument does not depend in any way on the properties of POVMs, which should you make deeply suspicious of your arguments having anything to do with them.

 

[Demystifier]

Instead you make strong assumptions about arbitrary measurements that go far beyond what has been demonstrated in the literature (where always a nondemolition assumption was involved to get decoherence).

I'm not sure I understand your point. Are you saying that in the literature only the non-demolition is assumed, while I assume something additional? What is this additional assumption that I make?

 

[A. Neumaier]

I'm not sure I understand your point. Are you saying that in the literature only the non-demolition is assumed, while I assume something additional? What is this additional assumption that I make?

No. You make fewer assumptions but pretend that essentially the same results follow, without telling why this should be so.

 

[Demystifier]

No. You make fewer assumptions but pretend that essentially the same results follow, without telling why this should be so.

I make fewer explicit assumptions, but the assumptions are implicitly there. That's because I think like physicist, not mathematician, so I try to explain how nature works, not to present a mathematical proof. I don't make explicit assumptions which seem obvious to me from a physical point of view, because I see such details as distraction from really important ideas. But I perfectly understand that you, as a mathematician, don't like this type of reasoning.

 

[A. Neumaier]

I make fewer explicit assumptions, but the assumptions are implicitly there. That's because I think like physicist, not mathematician, so I try to explain how nature works, not to present a mathematical proof. I don't make explicit assumptions which seem obvious to me from a physical point of view, because I see such details as distraction from really important ideas. But I perfectly understand that you, as a mathematician, don't like this type of reasoning.

I am not requiring mathematical rigor. But physics has a long and successful tradition in giving proofs at a high level, a level missing in your paper. You make suggestions, which might motivate why the results could possibly be true, but fail to give arguments that would satisfy anyone who really wants to understand what is behind. Your references to the literature only cover conditions where much stronger assumptions are needed to actually make a convincing justification.

In any case, nothing in your paper except for a few passing words relate to POVMs, thus making a further discussion of it off-topic in this thread.