In a discussion with someone recently, the person made the following statement:
Even when we observe a particle, it is still in superposition of position states within the resolution of the measurement
Now, according to what I've been taught, this is not true - a measurement will always yield a specific eigenstate of the system (eigenvector of the relevant self-adjoint operator corresponding to the observable), which the system will then be in. Yes, there will be some limit to the precision of the measurement, but this is not the same as the system still being in a superposition of position states.
It seems to me that this is obvious if we consider the conceptually simpler case of e.g. a Stern-Gerlach experiment, where we can unambiguously measure the particles as being in the spin up or down state (because we have a discrete spectrum of states).
I didn't want to disagree with the person because they are an expert on quantum information/compuation. Am I missing something here? Is the quote above true in some sense that I don't understand?
The broader context is that I took issue with the person stating that 'particles can be in two positions at the same time'. I take this to be an unfortunate and imprecise use of language - the notion seems semantically vacuous to me, unless we take it to be a trivial synonym for 'being in a linear combination of two position eigenstates at the same time'.