The quantum state cannot be interpreted statistically?

[bohm2]

This is an aside (and way too early) but if the "theorem" of that paper is correct would that imply that one is left with either the Everett or de Broglie/Bohmian versions?

 

[Ken G]

I don't really have a problem with that. If I thought the rest of the argument was sound, I would be pointing out that it's not obvious that such a theory exists, but I would still find their result interesting.

The key issue here is whether we should regard quantum mechanics as incomplete compared to a physical theory that would be possible (Einstein's view), or simply incomplete compared to our naive preconceptions about what a physical theory ought to be (i.e., we should not expect to completely represent the properties of a system with a mathematical object, either because the properties can't be represented that way, or don't exist in the first place). The article appears to consider it a "mild assumption" to take the former view, so does so, and shows that the ensemble view is inconsistent with that view. But I see nothing inconsistent in the ensemble view with the latter stance, and to me, the key question is not ensemble vs. real state, it is that first issue. So if we must take a stance on the first issue to follow their proof, then we have already ducked the most important question.

What bothers me is that they're saying that if the second view of QM (the statistical one) is correct, i.e. if a state vector doesn't accurately represent the properties of a single system, then the state vector isn't determined by λ.

That is OK within the assumptions they are making to give their argument. They are saying that if there are "properties" of individual systems, then either knowledge of the properties suffices to specify the state vector, or it doesn't. If it does, then each state vector has a correspondence to its own unique possible collection of properties-- i.e., if there are properties of individual systems, then the state vector limits the possibilities for those properties, so it does convey information about individual systems. If knowledge of the properties doesn't uniquely specify the quantum state, then it must be possible for the same properties to be associated with two different state vectors. That's what they use to get a contradiction. I think they are saying that if two state vectors connect with all different properties, those vectors have to be orthogonal, but by assumption they have two states that are not orthogonal, so they must have properties that appear with both state vectors-- unless the state vectors are themselves properties.

But if I was a proponent of the ensemble interpretation, I would simply claim that the whole reason I need an ensemble interpretation is that individual systems don't have properties like that! The "true state" of a system is not just a collection of eigenvalues for experiments we can think to do on it. (Whereas if I thought they did have properties like that, I'd call them hidden variables, and take the deBroglie-Bohm approach rather than the ensemble interpretation anyway.)

 

[qsa]

Ken, please check your PM , maybe something of an interest to you, related to this material.

 

[Fredrik]

The key issue here is...

I'm not sure I understood what you consider the key issue. Is it the existence (vs. non-existence) of that theory in which a mathematical object λ represents all the properties of the system? That's an interesting issue, but (as you know) it's not what the article is about.

If knowledge of the properties doesn't uniquely specify the quantum state, then it must be possible for the same properties to be associated with two different state vectors. That's what they use to get a contradiction.

Right. That's the part of the argument that I summarized as "If properties do not determine probabilities, then we're screwed. Therefore, properties determine probabilities." I have no problem with that part of it. In fact, I consider "properties do not determine probabilities" to be an absurd statement on its own. They didn't even have to derive a contradiction from it. (If λ doesn't determine all the probabilities (and then some), then why would anyone call it "all the properties of the system"). To me, their argument is very much like proving that 1≠1 implies that 2≠2, and then concluding that "Sons of Anarchy" isn't the best thing on TV right now.

I have always been thinking that the statistical view (ensemble interpretation) and "properties determine probabilities" are both true. It has never even occurred to me to consider that a complete specification of all the system's properties would be insufficient to determine the probabilities. Where did they get the idea that the statistical view implies that properties are insufficient to determine probabilities? I don't think it implies anything like that. What it says is that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).

 

[qsa]

I'm not sure I understood what you consider the key issue. Is it the existence (vs. non-existence) of that theory in which a mathematical object λ represents all the properties of the system? That's an interesting issue, but (as you know) it's not what the article is about.


Right. That's the part of the argument that I summarized as "If properties do not determine probabilities, then we're screwed. Therefore, properties determine probabilities." I have no problem with that part of it. In fact, I consider "properties do not determine probabilities" to be an absurd statement on its own. They didn't even have to derive a contradiction from it. (If λ doesn't determine all the probabilities (and then some), then why would anyone call it "all the properties of the system"). To me, their argument is very much like proving that 1≠1 implies that 2≠2, and then concluding that "Sons of Anarchy" isn't the best thing on TV right now.

I have always been thinking that the statistical view (ensemble interpretation) and "properties determine probabilities" are both true. It has never even occurred to me to consider that a complete specification of all the system's properties would be insufficient to determine the probabilities. Where did they get the idea that the statistical view implies that properties are insufficient to determine probabilities? I don't think it implies anything like that. What it says is that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).

I have a problem with ensemble interpretation, it is as if the equations know how we are going to study QM i.e. by doing experiments on prepared systems.

 

[Fredrik]

OK, new summary. Simplified.

They are comparing two different schools of thought:

1. A state vector represents the properties of the system.
2. A state vector represents the statistical properties of an ensemble of identically prepared systems, and does not also represent the properties of a single system.

Their argument against the second view goes roughly like this:

Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that view 2 above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false.​

I say that

• The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)
• The brown statement is a non sequitur. (A conclusion that doesn't follow from the premise).
• The only argument the article offers in support of the brown claim, doesn't support the brown claim at all.

Am I wrong about something?

 

[martinbn]

OK, new summary. Simplified.

They are comparing two different schools of thought:

1. A state vector represents the properties of the system.
2. A state vector represents the statistical properties of an ensemble of identically prepared systems, and does not also represent the properties of a single system.

Their argument against the second view goes roughly like this:

Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that view 2 above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false.​

I say that

• The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)
• The brown statement is a non sequitur. (A conclusion that doesn't follow from the premise).
• The only argument the article offers in support of the brown claim, doesn't support the brown claim at all.

Am I wrong about something?

I am probably missing something, but isn't the statement in brown what the difference between the two schools of thought is?

 

[Fredrik]

I am probably missing something, but isn't the statement in brown what the difference between the two schools of thought is?

That's what the authors of the article are saying. To me it seems like a completely unrelated assumption. Maybe I'm missing something.

I would say that the difference is that the second school of thought asserts that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).

 

[bohm2]

They are comparing two different schools of thought:

A state vector represents the properties of the system.
A state vector represents the statistical properties of an ensemble of identically prepared systems, and does not also represent the properties of a single system.

Isn't the bolded part the problem or am I missing something?

 

[qsa]

so they are going for the realist position, is that correct ?

 

[Fredrik]

Isn't the bolded part the difference or am I missing something?

That's definitely the difference. So no, you're not missing anything. But since the article claims that this difference changes the truth value of the statement

"The properties determine the probabilities."​

from true to false, the story doesn't end with that observation.

 

[DevilsAvocado]

Am I wrong about something?

I don’t know because I haven’t read the full paper yet (isn’t this just typical ), but is this really about ensembles (and the Ensemble interpretation)? Isn’t it about "state-as-probability" vs. "state-as-physical"?

I’ve cheated, and consumed the 'condensed version' by David Wallace (thanks inflector) and it looks convincing to me:

http://blogs.discovermagazine.com/c...lace-on-the-physicality-of-the-quantum-state/

Why the quantum state isn’t (straightforwardly) probabilistic
...
Consider, for instance, a very simple interference experiment. We split a laser beam into two beams (Beam 1 and Beam 2, say) with a half-silvered mirror. We bring the beams back together at another such mirror and allow them to interfere. The resultant light ends up being split between (say) Output Path A and Output Path B, and we see how much light ends up at each. It’s well known that we can tune the two beams to get any result we like – all the light at A, all of it at B, or anything in between. It’s also well known that if we block one of the beams, we always get the same result – half the light at A, half the light at B. And finally, it’s well known that these results persist even if we turn the laser so far down that only one photon passes through at a time.

According to quantum mechanics, we should represent the state of each photon, as it passes through the system, as a superposition of “photon in Beam 1″ and “Photon in Beam 2″. According to the “state as physical” view, this is just a strange kind of non-local state a photon is. But on the “state as probability” view, it seems to be shorthand for “the photon is either in beam 1 or beam 2, with equal probability of each”. And that can’t be correct. For if the photon is in beam 1 (and so, according to quantum physics, described by a non-superposition state, or at least not by a superposition of beam states) we know we get result A half the time, result B half the time. And if the photon is in beam 2, we also know that we get result A half the time, result B half the time. So whichever beam it’s in, we should get result A half the time and result B half the time. And of course, we don’t. So, just by elementary reasoning – I haven’t even had to talk about probabilities – we seem to rule out the “state-as-probability” rule.

Indeed, we seem to be able to see, pretty directly, that something goes down each beam. If I insert an appropriate phase factor into one of the beams – either one of the beams – I can change things from “every photon ends up at A” to “every photon ends up at B”. In other words, things happening to either beam affect physical outcomes. It’s hard at best to see how to make sense of this unless both beams are being probed by physical “stuff” on every run of the experiment. That seems pretty definitively to support the idea that the superposition is somehow physical.

 

[Fredrik]

I don’t know because I haven’t read the full paper yet (isn’t this just typical ), but is this really about ensembles (and the Ensemble interpretation)? Isn’t it about "state-as-probability" vs. "state-as-physical"?

That's the same thing.

"state-as-probability" = "ensemble interpretation" = "statistical interpretation" = "Copenhagen interpretation" (although some people will insist that the CI belongs on the "state-as-physical" side).

The stuff I'm talking about is covered on the first one and a half pages, so you don't have to read the whole thing. I haven't, and I'm not going to unless someone can convince me that I'm wrong.

But on the “state as probability” view, it seems to be shorthand for “the photon is either in beam 1 or beam 2, with equal probability of each”.

Maybe it seems that way, but this is not implied by my definition of the second "school of thought" above.

This is however a point that different statistical/ensemble interpretations disagree about. Ballentine's 1970 article "The statistical interpretation of quantum mechanics" explicitly made the assumption that all particles have well-defined positions, even when their wavefunctions are spread out. That assumption is notably absent from Ballentine's recent textbook, so maybe even he has abandoned that view.

 

[alxm]

I'll try again..

The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)

The way I read it, what they mean by "all the properties" is some set of hidden variables or similar that are sufficient to determine the outcome of any measurement. The "real" state is represented by lambda, and the quantum state is just a classical statistical distribution over the various "lambda states". It's not a classical analogy, it is classical. Although whatever goes into putting the system into a particular lambda state is not necessarily deterministic or local or whatever; only point is that QM tells us that certain processes will allow us to prepare states with certain distributions.

So knowing lambda doesn't tell you how you got there. A coin's 'real' states could be 'heads' or 'tails' but measuring 'heads' doesn't tell you if you got it there by putting it in heads (process 1) or a coin-toss (process 2). All you know from QM is that process 1 will always cause you to measure 'heads' and process 2 results in either 'heads' or 'tails' with some associated probabilities.

By extension the main result here is that for two identical systems prepared in isolation from each other, the result predicted by quantum mechanics for a joint measurement cannot be enforced merely by knowing lambda1 and lambda2, since it doesn't tell you how you got it there, which has importance for what you measure.

But if lambda is actually the wave-function (or can tell you it), then obviously there's no problem.

I didn't really think it was that complicated? Maybe I'm the one under-thinking it.

 

[DevilsAvocado]

That's the same thing.

"state-as-probability" = "ensemble interpretation" = "statistical interpretation" = "Copenhagen interpretation" (although some people will insist that the CI belongs on the "state-as-physical" side).

The stuff I'm talking about is covered on the first one and a half pages, so you don't have to read the whole thing. I haven't, and I'm not going to unless someone can convince me that I'm wrong.

I’ll do that tomorrow. It’s 3:32 AM here so my brain is in an upside-down-superposition...

Maybe it seems that way, but this is not implied by my definition of the second "school of thought" above.

This is however a point that different statistical/ensemble interpretations disagree about. Ballentine's 1970 article "The statistical interpretation of quantum mechanics" explicitly made the assumption that all particles have well-defined positions, even when their wavefunctions are spread out. That assumption is notably absent from Ballentine's recent textbook, so maybe even he has abandoned that view.

Okay thanks. I have to reconnect tomorrow, I’m really... :zzz:

 

[StevieTNZ]

What I gathered from reading the article at work:
1. they're assigning a definite state to the system after preparation
2. QM would then NOT be appropriate for describing the system - it is not in a pure state.
3. and the first experiment they show us gives a prediction different to QM, yet they're using it as refuting the statistical interpretation of QM - but I don't get that. They're practically saying QM is wrong.
4. on page 4, they use the conclusion as an assumption (a premise) in their argument.

 

[Ken G]

I'm not sure I understood what you consider the key issue. Is it the existence (vs. non-existence) of that theory in which a mathematical object λ represents all the properties of the system? That's an interesting issue, but (as you know) it's not what the article is about.

Right, I'm saying that to me, that's the real issue here. So I don't find the conclusions in the article to be particularly important, because they require making assumptions that I doubt are reliable. It seems to me that people who make those assumptions have already chosen a specific approach to interpreting quantum mechanics, so whether or not the ensemble interpretation is consistent with that specific approach is only interesting to people inclined to choose both the ensemble interpretation and that specific approach (and I don't count myself in either of those groups). But we can still analyze whether the paper reaches valid conclusions that people in both those groups should worry about.

Right. That's the part of the argument that I summarized as "If properties do not determine probabilities, then we're screwed."

But we aren't screwed in that case, we're just fine. If someone writes an article tomorrow that proves that quantum mechanics is not consistent with the attitude that properties determine probabilities, does quantum mechanics suddenly not work to predict our experiments? Nothing that we use quantum mechanics for requires that properties determine probabilities, instead what we need is for state vectors to determine probabilities, because that's how quantum mechanics works. Properties are completely irrelevant to doing physics, they are purely philosophical, and somewhat naive philosophy at that. That's my primary objection-- the fixation on the importance of "properties" is a very specific interpretation choice, but physics only requires that "properties" be a useful organizational principle, it never requires that we take this concept seriously, and certainly doesn't need us to make any mathematical proofs based on the notion. I doubt that systems actually have properties at all, that's just how we like to think about them.

The whole issue reminds me of Hume's lucid critique of taking the cause and effect relationship too seriously. He makes the point that even young children quickly develop a useful concept of cause and effect, but even the greatest philosophers cannot demonstrate any logical relationship there that you could use to prove anything, it is nothing but a practical correlation that we use to make actionable predictions. I think the concept of a "property" is just exactly like that too. So if someone hands me a physics proof that starts with "assume that the cause and effect relationship is a deterministic connection whereby some element of the cause leads, not by experience but by logical necessity, to some element of the effect", and goes on to say that interpretation X of theory Y can't be right, it is no kind of knock on interpretation X. Indeed, it makes me see interpretation X in a better light, that it failed to pass a test that it probably should fail!

In fact, I consider "properties do not determine probabilities" to be an absurd statement on its own.

It's not absurd if the whole concept of properties is already viewed as absurd. I agree it would be absurd to believe in properties that do not determine probabilities, for what would be the point in believing in properties like that, but the rational alternative is to view the whole "property" concept as an effective notion we create to make progress, like all the other effective notions we make in physics and should certainly have learned by now not to take so seriously as to prove things based on them as axioms. Or put differently, when we use them as assumptions and prove things, we should do it from the point of view of showing why we shouldn't have assumed that thing in the first place-- it forces us to imagine we are dictating to nature.

I have always been thinking that the statistical view (ensemble interpretation) and "properties determine probabilities" are both true. It has never even occurred to me to consider that a complete specification of all the system's properties would be insufficient to determine the probabilities. Where did they get the idea that the statistical view implies that properties are insufficient to determine probabilities?

This is an important question, and demands closer scrutiny. They seem to be saying they have proven that your position is internally inconsistent-- you cannot maintain both that a state vector is only a claim on the properties of an ensemble, not a claim on the properties of an individual system, and that properties of individual systems determine the probabilities for that system. I'm not sure exactly what they think the statistical interpretation is, but the one you expound sounds like a standard version, so they must feel that they have proven it to be internally inconsistent.

What it says is that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).

That's my point too, because quantum mechanics (and physics) only involves a connection between a preparation procedure and probabilities. That's it, that's all the physics that's in there. There aren't any "properties" in the physics, that's some kind of added philosophical baggage that can be used to prove things but doesn't convince me it belongs there at all, so why should we care what can be proven from it?

 

[bohm2]

That's my point too, because quantum mechanics (and physics) only involves a connection between a preparation procedure and probabilities. That's it, that's all the physics that's in there. There aren't any "properties" in the physics, that's some kind of added philosophical baggage that can be used to prove things but doesn't convince me it belongs there at all, so why should we care what can be proven from it?

I finally read the paper and I'm still lost. It seems to me that in this quote below the authors are conceding that if one takes that perspective you are suggesting (e.g. Fuchian) then their conclusions don't hold. If that's true then what does their theory suggest?

For these reasons and others, many will continue to hold that the quantum state is not a real object. We have shown that this is only possible if one or more of the assumptions above is dropped. More radical approaches (e.g. Fuchs) are careful to avoid associating quantum systems with any physical properties at all.

Their assumptions:

1. If a quantum system is prepared in isolation from the rest of the universe, such that quantum theory assigns a pure state, then after preparation, the system has a well defined set of physical properties.

2. It is possible to prepare multiple systems such that their physical properties are uncorrelated.

3. Measuring devices respond solely to the physical properties of the systems they measure.

 

[StevieTNZ]

Their assumptions:

1. If a quantum system is prepared in isolation from the rest of the universe, such that quantum theory assigns a pure state, then after preparation, the system has a well defined set of physical properties.

I am assuming that by a 'well defined set of physical properties' that the system is in a definite state? That is the impression I'm getting from what they wrote under Figure 1, that the system is in either |0> or |1>.

You CANNOT use QM to predict the outcomes, clearly. QM doesn't deal with definite states. In the first experiment, they produce results different to what QM predicts.

And just looking at some of what they wrote, where do they get |-> from?

 

[Fredrik]

I have to go to bed, so my answers to the stuff aimed at me will have to wait until tomorrow. Alxm's post gave me something to think about. It looks like I have misunderstood at least one important thing, so I will have to think everything through again.

I am assuming that by a 'well defined set of physical properties' that the system is in a definite state? That is the impression I'm getting from what they wrote under Figure 1, that the system is in either |0> or |1>.

No, either |0> or |+>. The latter is a superposition of |0> and |1>. |0> and |1> are the eigenstates of some operator, like a spin component operator. But they have one preparation device that always leaves the system in state |0> and another that always leaves the system in state |+>.

 

[StevieTNZ]

Man, I'm an idiot! Where did I get |1> for |+>?!

 

[DevilsAvocado]

[my bolding]

... By extension the main result here is that for two identical systems prepared in isolation from each other, the result predicted by quantum mechanics for a joint measurement cannot be enforced merely by knowing lambda1 and lambda2, since it doesn't tell you how you got it there, which has importance for what you measure.

But if lambda is actually the wave-function (or can tell you it), then obviously there's no problem.

Isn’t this exactly what David Wallace describes in his simple https://www.physicsforums.com/showthread.php?p=3623347#post3623347"?

 

[Physics Monkey]

Two comments/questions:

1. Although I have seen various people claim an equivalence between "the statistical interpretation" and what they are calling view 2, I don't understand this claim. This looks to be similar to what Fredrik is saying. Don't physical properties include the probability distributions of all possible probes of the system?

2. Related to 1., it seems like I can understand their paper as giving me a particular experimental method to (more fully) determine $\lambda$ using additional experiments on composite systems.

For example, in the paragraph beginning "The simple argument is ...", sentence 3 is particularly interesting. Can we not argue that $q$ is zero since their later experiment can determine which of the two preparations was used? In other words, aren't they proving that we can always determine the "preparation method"? This is partially predicated on my confusion in 1. about why the "preparation method" story is equivalent to the statistical interpretation.

 

[alxm]

[my bolding]
Isn’t this exactly what David Wallace describes in his simple https://www.physicsforums.com/showthread.php?p=3623347#post3623347"?

Well, the conclusion is the same. But it seems to me that he's more describing the ordinary double-slit experiment.

One key difference between that and what's being described in the paper, is that the states of the double-slit/half-silvered mirror paths aren't created independently of each other. It's quite a bit less weird to have "spooky action at a distance" between a single state "split" in two, than between two states prepared in isolation that never had any interaction. That's what seems to be the main novelty here.

 

[Fredrik]

The way I read it, what they mean by "all the properties" is some set of hidden variables or similar that are sufficient to determine the outcome of any measurement. The "real" state is represented by lambda, and the quantum state is just a classical statistical distribution over the various "lambda states". It's not a classical analogy, it is classical. Although whatever goes into putting the system into a particular lambda state is not necessarily deterministic or local or whatever; only point is that QM tells us that certain processes will allow us to prepare states with certain distributions.

So knowing lambda doesn't tell you how you got there.

Thanks for posting this. This is a very nice explanation. I've been thinking that they probably meant something other than this, since they weren't very explicit about it. Now I'm thinking that this must have been what they meant.

I thought that they were leaving it undefined what it means for λ to represent all the properties of the system. Now I think that they are using a definition of "property" similar to this one:

A property of the system is a pair (D,d) (where D denotes a measuring device and d denotes one of its possible results) such that the theory predicts that if we perform a measurement with the device D, the result will certainly be d.​

To say that λ represents all the properties is to say that the super-awesome classical theory that λ is a part of can predict the result of every possible measurement.

I will do some more thinking and post a new summary when I have something.

 

[zonde]

Ensemble interpretation says that QM works for ensembles but does not work for individual systems.
This paper under discussion says that indeed ensemble interpretation leads to contradiction if QM is applicable to individual systems (thought experiment in fig.1). So what?

Or in terms of properties. Quantum state is determined by properties of ensemble that include properties of individual systems and emergent properties. Then certain properties of individual systems can correspond to different quantum states but that does not mean that there is any ambiguity in correspondence between quantum state and properties of ensemble.

 

[DarMM]

So quantum mechanics is non-commutative probability. The basic problem we have with these probilities is interpeting them, early work of Von Neumann was directed at showing that non-commuting probabilities don't results as probability distributions over some classical theory.

The strongest result in this regard is the Kochen-Specker theorem which says that if there is a real deterministic theory underneath QM with matter in some state λ, then that theory can only model quantum mechanics if it allows contextuality (which basically implies non-locality in a relativistic theory). Basically QM can only be the statistical mechanics of some underlying "true" classical theory if that theory has faster-than-light signalling.

However this new paper appears to be pushing even further, saying that even contextual theories don't work and QM can't be seen as the statistical mechanics of any deterministic theory. Whether it actually does this remains to be seen.

 

[DevilsAvocado]

Well, the conclusion is the same. But it seems to me that he's more describing the ordinary double-slit experiment.

One key difference between that and what's being described in the paper, is that the states of the double-slit/half-silvered mirror paths aren't created independently of each other. It's quite a bit less weird to have "spooky action at a distance" between a single state "split" in two, than between two states prepared in isolation that never had any interaction. That's what seems to be the main novelty here.

Okay, thanks!


P.S. Although I’m sure that DrC can convince you that there’s absolutely nothing 'weird' about entanglement between objects that never had any interaction...

 

[DevilsAvocado]

Ensemble interpretation says that QM works for ensembles but does not work for individual systems.
This paper under discussion says that indeed ensemble interpretation leads to contradiction if QM is applicable to individual systems (thought experiment in fig.1). So what?

So what? You are also claiming "that there is difference between statistical "sum" of 1000 experiments with single photon and single experiment with 1000 photons".

So how can I take you seriously?

 

[juanrga]

This is wrong, and it's also a very different claim from the one made by this article. A state vector is certainly an accurate representation of the properties of an ensemble of identically prepared systems. It's conceivable that it's also an accurate representation of the properties of a single system. The article claims to be proving that it's wrong to say that it's not a representation of the properties of a single system.

This is even more wrong. Also, if you want to discuss these things, please keep them to the other thread where you brought this up.

As the first postulate of QM states clearly, the pure quantum state describes the state of a physical system, not of an ensemble.

The so-called «statistical interpretation» is wrong as both this paper and the link given by me before show. The paper is also right when it points that the «statistical interpretation» was introduced for eliminating the collapse of the quantum state. But this collapse is a real process, which is described by the von Neumann postulate, in QM, and by dynamical equations in more general formulations beyond QM.

I remark again that the paper is right: the quantum pure state is not «akin to a probability distribution in statistical mechanics», as some ill-informed guys still believe.

As any decent textbook in QM explains, ensembles in quantum theory are introduced by impure states not by pure states.