Comparison between quantum entanglement and a classical version

[Mentz114]

And that what made EPR-experiment a paradox.
But if we adopt the simple interpretation that only the difference between detectors angles matters, no paradox appears. In this interpretation, faster than light speed is not required because a causal influence on Bob spin-state from Alice`s wave-function collapse is not required too. What is required is a universal "space awareness" which is a knowledge about the difference between detectors angles in two space-like events. As if there is an additional term in 4D Minkowski space equation that when switching to "quantum mode" cancels the time metric and reduced it to Galilean 3D space equation. That makes me think that EPR-experiment is a real test for special relativity not for quantum theory.

I don't think that is correct. Introducing an extra dimension ( if that is what you propose ) has the same effect as a NLHV theory but no physical justification.

 

[Adel Makram]

There is no EPR "paradox" - no apparent contradictions appear anywhere in the EPR argument.

https://en.wikipedia.org/wiki/EPR_paradox

So in your opinion, how to explain the outcomes of Alice Bob spins-experiment and quantum correlation based on causality or based on anything?

 

[Adel Makram]

It is only when they compare their results and compute the correlation that they can decide that something non-classical has taken place.

But the quantum correlation is valid whether they compare or not, isn't it? Like two men (European and Asian) know they have two different time zones whether they compare their watches or not.

 

[Heinera]

But the quantum correlation is valid whether they compare or not, isn't it? Like two men (European and Asian) know they have two different time zones whether they compare their watches or not.

The quantum correlation is valid in the sense that this is the outcome QM predicts for the computation of the correlation. If you are contemplating what the prediction is for an uncomputed correlation, then we are moving towards methaphysical territory. My point was that if Alice and Bob don't compare their results and never compute the correlation, they could just as well explain their isolated results with a classical theory, so no instant signalling is possible.

 

[Adel Makram]

My point was that if Alice and Bob don't compare their results and never compute the correlation, they could just as well explain their isolated results with a classical theory, so no instant signalling is possible.

This is not my point. My point is quantum correlation will not involve faster than light signaling therefore it will not invalidate SR. But quantum entanglement ( spooky action) requires a more generalized theory than SR because it doesn't necessary involve signal transmission. For example, GR is more general than SR because if the mass energy tensor =0, GR reduced to SR but this does not mean that SR is invalid. It means it is not general enough to explain the physics if there is a gravitational mass.

 

[Simon Phoenix]

So in your opinion, how to explain the outcomes of Alice Bob spins-experiment and quantum correlation based on causality or based on anything?

I don't understand your question.

One way to phrase the locality condition for this experiment is that results 'here' do not depend on settings 'there'. This is true in QM too (if it weren't true we'd be able to use this to construct a FTL communication scheme).

Another way to see this is the following. We'll consider 2 experiments
(1) Alice is given a spin-1/2 particle uniformly randomly selected to be spin up or spin down
(2) Alice is given one spin-1/2 particle from a maximally entangled pair of spin-1/2 particles
She receives a particle but is not told whether it is from experiment (1) or experiment (2)

There is no measurement Alice can do on her particle alone that will enable her to determine whether it is experiment (1) or experiment (2).

 

[Heinera]

This is not my point. My point is quantum correlation will not involve faster than light signaling therefore it will not invalidate SR. But quantum entanglement ( spooky action) requires a more generalized theory than SR because it doesn't necessary involve signal transmission. For example, GR is more general than SR because if the mass energy tensor =0, GR reduced to SR but this does not mean that SR is invalid. It means it is not general enough to explain the physics if there is a gravitational mass.

But why should quantum entanglement require a more generalized theory than SR, as long as it already is consistent with SR? No FTL communication is possible with quantum entanglement, in agreement with SR.

 

[Adel Makram]

But why should quantum entanglement require a more generalized theory than SR, as long as it already is consistent with SR? No FTL communication is possible with quantum entanglement, in agreement with SR.

Ok. So how SR explains the non locality then?

 

[Simon Phoenix]

Ok. So how SR explains the non locality then?

What non-locality?

Could you explain precisely what it is about QM that you see as non-local?

There is nothing Alice can do locally that in any way affects, superluminally, the results of a distant measurement - this is true in QM too. So what is it you're seeing as being 'non-local'?

 

[Heinera]

Ok. So how SR explains the non locality then?

If by "non locality" you mean the violation of Bell's inequality, then SR does not need to explain it, since it is consistent with SR. The closest you come to an explanation is in QM itself, from the fact that the wave function of the two particles depends on both, even when they are spatially separated. But QM gives no deeper explanation than that, something which is left to the interpretations. You could have an interpretation that says that QM is a quasi-classical model that requires instant signalling in a hidden layer, but of a kind that could never be used for proper communication (so that SR would still hold). But it would only be pure speculation, since no empirical test could uncover this hidden layer.

 

[Nugatory]

https://en.wikipedia.org/wiki/EPR_paradox

Yes, you will often hear the word "paradox" applied to the EPR argument. However, EPR themselves do not use that word and it doesn't even appear in the paper. Instead, they argue a syllogism: All complete theories have certain properties; QM does not have one of those properties; therefore QM is not a complete theory. It turns out that their major premise is mistaken (whatever complete theory we end up, whether QM or something else, will not have all of these properties), but this was not apparent at the time and didn't become apparent until decades later.

So in your opinion, how to explain the outcomes of Alice Bob spins-experiment and quantum correlation based on causality or based on anything?

You pick an interpretation of quantum mechanics and use whatever explanation that interpretation suggests. There's an interesting discussion of some of these issues at http://arxiv.org/abs/quant-ph/0212140.

 

[Adel Makram]

What non-locality?

Could you explain precisely what it is about QM that you see as non-local?

There is nothing Alice can do locally that in any way affects, superluminally, the results of a distant measurement - this is true in QM too. So what is it you're seeing as being 'non-local'?

Non locality means Bob particle changed to a definite spin state when Alice particle measured instantaneously according g to the collapse interpretation.

 

[Adel Makram]

Suppose there are two experiments set ups, one allows Bob to measure the expected outcome Of his measurment of spin direction from a singlet state and the other from an entangled state.
Knowing nothing about whether Alice, Bob measures his spin direction, up-down, and take the average. If the experiment set up is a singlet one, then Bob would have a 50% chance to have a spin up. If, instead the set up is entangled and Alice exists to the other side of the world pointing her detector to a direction antiparallel to Bob' one then Bob measures his spin up in 100% of times. Now Bob comes to know that not only the spin state s entangled but he knows the direction where Alice points her detector. They can even communicate using different angles as an agreed alphabet although no physical signal is used.

 

[Adel Makram]

I know that saying Bob measures his spin up in 100% of times sound contradictory with what have been discussed here when we say Alice has a 50% chance to measure her spin because there should nor be any preference of Alice on Bob. But I don't know how to clear this so.

 

[Simon Phoenix]

Bob to measure the expected outcome Of his measurment of spin direction from a singlet state and the other from an entangled state.

A singlet state is just the name given to a particular kind of entangled state - usually the state that looks like ~ |01> + |10>

If, instead the set up is entangled and Alice exists to the other side of the world pointing her detector to a direction antiparallel to Bob' one then Bob measures his spin up in 100% of times

No. That's completely incorrect. Sure Bob's result will be correlated with Alice's, but Alice's result is random.

 

[Simon Phoenix]

Non locality means Bob particle changed to a definite spin state when Alice particle measured instantaneously according g to the collapse interpretation.

As others have pointed out - there's a problem with using some notion of collapse here. Is it Alice or Bob who collapses the state? The answer is that it could be either depending on the frame of reference. So there's something a bit wonky with this idea that measurement causes some state change (collapse) in this scenario.

But even so it's important to realize that the issue only occurs because of a particular interpretation we've placed on things and not really a feature of QM.

Strip away the interpretative fun and games and QM is a theory that links preparations with measurement results - that's all. It doesn't tell us what's "really" happening in between these two things in any definite sense. Some people advocate thinking of the state, or wavefunction, as merely an abstract mathematical device that possesses no physical reality. It just allows us to calculate correct measurement probabilities. When we make a measurement we gain new information and so our probabilities instantly change - nothing at all non-local or strange about that process.

The point is that we don't actually need collapse as a concept in QM and nor do we need to think of the state as being some real physical entity that evolves.

Having said that, my own personal preference is to think in terms of measurement-induced collapses of a real physical entity, because that's the easiest and most pragmatic way of thinking about QM for me. But even so, there is no real issue with non-locality since no physical observables are being changed or linked by anything FTL - in other words there are no non-local experimental consequences. Only this nebulous wavefunction or state (whatever this might be) changes instantaneously in this perspective.

 

[Nugatory]

Non locality means Bob particle changed to a definite spin state when Alice particle measured instantaneously according to the collapse interpretation.

That is not what "non-locality" means.

Speaking loosely, non-locality refers to the fact that to calculate the result at either detector you need to know the settings of both detectors - any mathematical equation that correctly predicts the experimental results will include the angle between the two detectors somewhere. This non-locality does not necessarily conflict with relativity (although it will if you also assume wave function collapse, which is a good reason not to make that assumption).

Note that I did say "speaking loosely"... There are some subtleties here, and the Timson/Brown paper I linked above goes into them in more depth.

 

[stevendaryl]

Also if probability of Bob measuring spin down = sin² (β - Φ)/2)
And this formula is equated to 1/2 ( 1 - β ⋅ α ) above then can someone show this numerically also ?

It's just a trigonometric identity: sin^2(\frac{X}{2}) = \frac{1}{2}(1 - cos(X))

 

[stevendaryl]

Ok. So how SR explains the non locality then?

Well, that's what's tricky about QM. Although some interpretations (the collapse interpretation, the Bohm interpretation) involve faster than light interactions, there is no way to use QM to send a FTL signal, and so there is no way to use QM to demonstrate a violation of SR.

 

[Simon Phoenix]

Ok. So how SR explains the non locality then?

I think it's also useful to realize that we don't actually need non-locality to see a violation of the statistical inequality we call Bell's inequality, and nor do we need entanglement. If that seems counter to everything you've read on Bell's inequality then consider the following :

In the usual scenario we have Alice <---------------- Source ----------------> Bob
Let's bring Alice closer to the source so that we have Alice <- Source ---------------->Bob

In both these cases when statistics are compared we see a violation of the BI (for appropriately chosen measurement angles)

Now let's put the source in Alice's lab. She doesn't allow any of the entangled particles to reach Bob, but she makes a measurement of one of the entangled particles as she would in the normal set-up. Now she uses the result she obtains to prepare another spin-1/2 particle and sends this off to Bob

So we have || Alice <- Source -> || ......Bob
then Alice ---------------->Bob

So in fact we don't need the entangled source at all - Alice can just randomly prepare spin-1/2 particles in the appropriate states.

Now when we compare the statistics there's a violation of the Bell inequality but it's between Alice's state preparation and Bob's measurement.

No problems with FTL signals here - and we don't need entangled particles - yet we're still seeing a violation of a mathematical inequality (the BI)

Of course this is a different experimental set-up which doesn't carry with it the same implications for 'reality' - and it was the brilliance of EPR and subsequently Bell to focus on a simple physical system that could bring out these implications for 'reality' - but it's not the 'non-local' bit of QM (or the entanglement) that's actually giving us mathematics capable of violating the mathematical inequality. A bit hard to state precisely, sorry, but I hope you get my drift here.

 

[DrChinese]

Now let's put the source in Alice's lab. She doesn't allow any of the entangled particles to reach Bob, but she makes a measurement of one of the entangled particles as she would in the normal set-up. Now she uses the result she obtains to prepare another spin-1/2 particle and sends this off to Bob

So we have || Alice <- Source -> || ......Bob
then Alice ---------------->Bob

So in fact we don't need the entangled source at all - Alice can just randomly prepare spin-1/2 particles in the appropriate states.

Now when we compare the statistics there's a violation of the Bell inequality but it's between Alice's state preparation and Bob's measurement.

So you are saying exactly what? Bell inequalities demonstrate that local hidden variable explanations are not viable for some experiments. Yours isn't one of them.

 

[Simon Phoenix]

So you are saying exactly what? Bell inequalities demonstrate that local hidden variable explanations are not viable for some experiments. Yours isn't one of them.

Agreed :-)

I'm sorry I was hoping that I made it clear that this different experimental set-up doesn't have implications for reality in the same way that the usual Bell set-up does. My fault.

What I was trying to get at was that in both cases the maths is identical - just that we interpret it differently in each case. For me I think it brings out that the non-commutatitivity is driving the violation in QM - and when we apply this to the usual Bell set up we also get all these interesting implications for hidden variable theories.

In a nutshell there's nothing Bob can do even when given Alice's data to distinguish whether the results are from genuine entangled particles or Alice's state preparations. This has practical implications in that we can use this in a quantum key distribution using the Bell inequality protocol, but now with single particles instead of having to use entangled sources which are practically a bit trickier.

 

[Simon Phoenix]

I think there's also a sense in which the issue of non-locality is almost a red herring. That's a little bit of an overstatement and I hope the following will make it clearer what I mean.

If we impose the condition that results 'here' do not depend on settings 'there' even if here and there are only timelike separated, then a hidden variable theory of QM of this kind would satisfy the Bell inequality. We can't rule out a hidden variable theory of physics which did allow this. So even for timelike here and there we can rule out a certain class of local hidden variable theories.

So the possible candidate hidden variable theories are those in which information about settings 'there' is transferred to 'here' and affects results 'here'. I've not seen any of these constructions which look like anything like a 'sensible' theory of physics. They are possible, but somewhat artificial (at least the ones I've seen) - even in the local case where 'here' and 'there' are timelike separated. The Bohm theory, which is non-local anyway, has some attractive features and is perhaps the most 'natural' I've seen, but even there we have to introduce this complex guiding potential.

If anyone does know of a 'natural' local hidden variable theory that works (i.e. violates the BI) in this more restricted timelike case - then I'd love to see it if you have a link.

So in my view 'classical' physics is struggling even before we hit the issue of non-locality. In this case then I think it's useful to figure out what it is about QM that's causing the violation - even in the local case which only rules out a more restricted class of local hidden variable theories.

Of course it's critical that we go that last step and consider spacelike separated 'here' and 'there' - and then we put the final nail in the coffin of local hidden variable theories.

 

[Adel Makram]

If we impose the condition that results 'here' do not depend on settings 'there' even if here and there are only timelike separated, then a hidden variable theory of QM of this kind would satisfy the Bell inequality. We can't rule out a hidden variable theory of physics which did allow this. So even for timelike here and there we can rule out a certain class of local hidden variable theories.

So what class of local hidden variables that satisfies BI in a time-like experiment?

 

[Nugatory]

So what class of local hidden variables that satisfies BI in a time-like experiment?

Any theory in which the result at either detector depends on the initial state (hidden and unhidden variables) of the particle pair and on the state (hidden and unhidden variables) of that detector at the time detection will satisfy the inequality - that IS the theorem, restated in layman's language, as the theorem derives the inequality from the premise that the theory is as I just said. The timelike or spacelike separation of the measurement events is irrelevant to this proof.

 

[Adel Makram]

Will the quantum correlation be reproduced by putting 2 polarizers with opposite direction between the source and the detectors (one polarizer at each side of the source that pass only spin up along its direction) and repeating the experiments at different angles of both polarizers near the source and the polarizers at Alice and Bob?

Let`s put 2 polarizers, one on each side of the source, P<sub>toward Alice</sub> ( between the source and Alice) and P<sub>toward Bob</sub> ( between the source and Bob). The two polarizer are in opposite direction and they only pass spin-up along their respective direction so that the spin-up( up in the +ve Z direction) from P<sub>toward Alice</sub> is accompanied by spin-down (-ve Z) from P<sub>toward Bob</sub>.
Then Alice and Bob are measuring their spins at their detectors/polarizers as in standard Bell`s experiment with different angles of their detectors and compare their results. Will they come to a quantum correlation?
Let`s repeat the experiment by rotation the polarizers-set at many angles from 0 to 2π ( but always keeping them at opposite direction) and compare results again. Will the result be in keeping with quantum correlation?

Clearly the BI will be violated if we only compare P_{toward Alice} with the detector/polarizer at Bob or P_{toward Bob} with the detector/polarizer at Alice but how about the correlation between Alice and Bob outcomes?

On one hand, the correlation between Alice and Bob would be classical in nature because the spin status has been already collapsed at the polarizer near the source and the results at Alice and Bob places will be independent as if there would be taken at two non-entanged spins at different places.
On the other hand, the orientation of spins reaching Alice and Bob will be always in opposite direction and repeating experiment at different angles of the polarizer-set at the source with no information about which angle is choozen might be similar to the fully entanglement status which should mandate results in keeping with quantum correlation.
So where did I go wrong?

 

[Nugatory]

So where did I go wrong?

Alice's measurements will depend on the angle between her detector and the filtering device on her side, but not on Bob's settings. Likewise, Bob's results will depend on the angle between his detector and the filtering device on his side, but not on Alice's settings.

(You said "polarizer" but you're talking about particle spins not polarizations, so a polarizer is the wrong device to achieve your purpose. You need something like a Stern-Gerlach device, which deflects particles with spin-up along its axis in one direction and spin-down in the opposite direction).

 

[Adel Makram]

Alice's measurements will depend on the angle between her detector and the filtering device on her side, but not on Bob's settings. Likewise, Bob's results will depend on the angle between his detector and the filtering device on his side, but not on Alice's settings.

(You said "polarizer" but you're talking about particle spins not polarizations, so a polarizer is the wrong device to achieve your purpose. You need something like a Stern-Gerlach device, which deflects particles with spin-up along its axis in one direction and spin-down in the opposite direction).

So the correlation between Alice and Bob measurements will be classical.
But considering that both sides know nothing about the angle of the filtering device near the source relative to z-axis which is changing at random for each pair. This would simulate the mixed state of fully entangled particles, I expect the correlation to follow quantum mechanics prediction.

 

[Nugatory]

This would simulate the mixed state of fully entangled particles

The probability of Alice and Bob getting the same result will not be $\sin^2\frac{\alpha-\beta}{2}$. Bob and Alice will find this out when they get together afterwards and compare the results of their measurements.

 

[DrChinese]

But considering that both sides know nothing about the angle of the filtering device near the source relative to z-axis which is changing at random for each pair. This would simulate the mixed state of fully entangled particles, I expect the correlation to follow quantum mechanics prediction.

It will not simulate an entangled state at all. The stats may match at selectively chosen angles, but that's it. One is product state stats, the other is entangled state stats.