Recent content by Kolmo

I've read that before, but it seems to give some nice details about energy and scattering not a description for general operators. Also I've read a few criticisms of it, such as the inability to replicate multi-time correlations. Is there a presentation of the equivalence for general operators...

Where is it actually proven that it gives the same results for all observables. I've seen the proofs that with quantum equilibrium we get the same results for single particle position measurements, but I've never seen the proof of the general case.

I'm not saying pure states can evolve into mixed states under the Schrödinger equation, obviously they cannot. I'm saying that a macroscopic body is in a mixed state due being in thermal contact with some environment, interacting with EM fields and so on.

It didn't really matter for the main point I was making. My point was that a large component of quantum theory, i.e. the structure of the state space, the space of observables and so on were provably a probability theory in terms of their mathematical structure. I just used the word "kinematic"...

As I said above, a virus in real life is embedded in a thermal environment, it's characterised by values for macroscopic observables and so forth. All of these things give a mixed state as the correct state, not a pure state.

For a literal virus I wouldn't say it was "empty" as such, but certainly an incorrect state assignment, since an actual virus will be in thermal equilibrium with some environment, emitting EM radiation and so forth. Perhaps WernerQH means simply that. A state that is so wrong could be said to...

Addendum: More explicit in: G.Ludwig: “Geloeste und ungeloeste Probleme des Messprozesses in der Quantenmechanik”, in “W.Heisenberg und die Physik unserer Zeit”, ed. F.Bopp, Vieweg, Braunschweig 1961

I kind of understand what is being said here but two points. (a) In general the state afterward is not some eigenvalue of a observable, but rather updated via a Kraus operator. This isn't too important since the text might be focusing purely on von Neumann style measurements. (b) There's...

In general for a selection of properties one can construct pure states that give similar results to Gibb's states, but many statistical mechanical properties won't give the same results and in general the entanglement measures are not correct. If one is only concentrating on a small selection of...

It's important though that there is no such pure state, it is necessarily mixed. This is an important point in detailed models of measurement.

Weak measurements are just POVMs whose Kraus operators are close to the identity and possibly followed by post-selection. So yes essentially.

As mentioned above by vanhees71 and as seen in many models of measurements, the states of the device are of course in fact high-entropy mixed states, usually constructed by maxent methods or similar. The temperature example you give being a clear case, as a state of some temperature ##T## is a...

No. Models of measurement equally model POVMs, Weak Measurements and so on. The Curie-Weiss model of measurement which is the default "very detailed" measurement model naturally produces POVMs. So it's not restricted to optimal measurements.

Trying to think of a way to phrase this, but if that unitary evolution, given the observable algebra of the device, results in a classical probability distribution over the observed outcomes isn't that all you need. Each term can just be read off as a probabilistic weighting of given values of...

These theorems are interesting as a means of exploring how trustworthy or certifiable mesoscopic systems are in quantum circuits, but it's very overblown as something applying to real lab measurements.