# Quantum state vector and physical state

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1. Feb 15, 2016

### Staff: Mentor

Interesting new work on the link between quantum state vectors are physical states:

Can different quantum state vectors correspond to the same physical state? An experimental test
Daniel Nigg et al 2016 New J. Phys. 18 013007

Abstract
A century after the development of quantum theory, the interpretation of a quantum state is still discussed. If a physicist claims to have produced a system with a particular quantum state vector, does this represent directly a physical property of the system, or is the state vector merely a summary of the physicist's information about the system? Assume that a state vector corresponds to a probability distribution over possible values of an unknown physical or 'ontic' state. Then, a recent no-go theorem shows that distinct state vectors with overlapping distributions lead to predictions different from quantum theory. We report an experimental test of these predictions using trapped ions. Within experimental error, the results confirm quantum theory. We analyse which kinds of models are ruled out.

http://dx.doi.org/10.1088/1367-2630/18/1/013007

2. Feb 16, 2016

### vanhees71

Sounds interesting, but the title for sure is already a bit fishy. It should read

Can different rays in Hilbert space correspond to the same physical state? An experimental test

Of course, a state vector is determined from a pure quantum state, which is given by a projector $|\psi \rangle \langle \psi|$ with $|\psi \rangle$ a unit vector, only up to a phase. I'm sure another question than the one in the title is addressed in this paper ;-)). I hope I find the time to translate the abstract into physics this evening ;-)).

3. Feb 16, 2016

### DrChinese

Great follow-up paper to the original PBR paper. Amazing stuff. Thanks for posting.

Apparently, the state vector is "real" in the sense defined, while (counterfactual) observables themselves are not.

4. Feb 17, 2016

### vanhees71

Can you explain an ignorant particle/nuclear theorist as I am the point of this paper? I didn't get it. Different rays in Hilbert space define distinct pure states of a quantum system, and there are observable differences between them. That's the general scheme. On exception that comes to my mind are gauge theories, where a state is not only a ray but an entire "gauge orbit".

Taken aside these formalities. I even didn't get the introductory classical die example. He considers two different "events" (in the sense of usual probability theory a la Kolmogorov or equivalent), namely: $E_1$="the die shows an even numer" and $E_2$="the die shows a prime number". Than he assumes that for some strange reason the probality distributions are not the expected ones of a "fair" die but
$$P_1(n)=\begin{cases} 1/3 \quad \text{if} \quad n \quad \text{even}, \\ 1/3 \quad \text{if} \quad n \quad \text{odd}.\end{cases}$$
or
$$P_2(n)=\begin{cases} 1/3 \quad \text{if} \quad n \quad \text{prime}, \\ 1/3 \quad \text{if} \quad n \quad \text{non-prime}.\end{cases}$$
Of course, if an observer only knows that the probability that the die shows "2" is 1/3, he cannot distinguish these two probability distributions. But that doesn't imply that the two "preparations" of the die are the same. If he'd through the die often enough, he can figure out the probabilities for all numbers and thus very well distinguish the two "states", described by the distinct probability distributions.

Unfortunately I had not the time to analyze the physics case in the paper.