Quantum Entanglement for nonphysicists

[Ghidrah]

I'm trying to understand why entanglement is said to be "spooky."

The model I have is that 2 entangled particles are related, such that they have identical states when measured. The entanglement process is what ensures they have identical states. So it's no surprise they measure out the same.

For example, I could have 2 white and 2 black marbles in 4 opaque indistinguishable bags. I then put 2 bags containing white marbles in bag A, and the other 2 bags containing black marbles in bag B. Then I mix bag A and bag B so I cannot tell them apart. Then I select one bag (it is either A or B, but I do not know which.) I open it, and separate the two smaller "entangled" bags. I know they will be the same color, but not if that is black or white.

That's my model of quantum entanglement. It makes perfect sense classically.

What am I missing?

 

[Eye_in_the_Sky]

Your model implies locality, which itself implies that Bell's inequality
(E(2θ) ≤ 2E(θ), for all θ) is satisfied for the entangled particles. On the other hand, the quantum formalism implies that Bell's inequality is not satisfied (i.e. there exists θ, such that E(2θ) > 2E(θ)), which implies nonlocality. If you accept that "nonlocality" is "spooky", then this explains the query raised in your initial statement.

What you are missing in your consideration of the problem is every case where θ ≠ 0.

(Sorry, if my response is too cryptic to be understandable.)

 

[Ghidrah]

Is it even possible to describe entanglement in terms of bags and marbles then? (Yes, I did not understand your explanation at all. Sigh.)

I'll look up nonlocality and see if I can learn something.

Thanks for answering. Still looking for a description...

Aha. OK, it looks like I was really thinking about and wanting to understand nonlocality, and I've googled up some explanation of that I think I will understand tomorrow...

 

[Fredrik]

Is it even possible to describe entanglement in terms of bags and marbles then?

No, it's not. If the bags and marbles description were correct, the correlations would satisfy Bell inequalities, and they don't. This has been demonstrated by experiments.

 

[Claude Bile]

The entanglement process is what ensures they have identical states.

Entangled particles are not necessarily in identical states, for example degenerate photon pairs from three wave mixing processes must have opposite polarisations.

Measurement of one photon's polarisation, immediately forces the second degenerate photon to adopt the opposite polarisation. This effect is instantaneous, even if the two photons are very far apart.

The ability to change a photon's state without directly interacting with it, instantaneously, even if the photon is a few metres away, well, some find that pretty 'spooky'.

Claude.

 

[Integral]

The entangled particles do NOT have identical states, only states that are related in a manner determined by QM. As long as no particle is observed either particle can be in any of the possible states, as soon as one particle is observed the state of the other particle is determined.

Let us consider an experiment with normal marbles, suppose we have 3 marbles, Red, Yellow and Blue. If we blindly select 2 marbles and do an experiment on one of the selected marbles which tells only that it is NOT a certain color, say blue. What does that tell us of the color of the other marble? It could be either blue, red or yellow. If we repeated this experiment many times we would expect a uniform distribution between red, yellow and blue, 1/3 for each color.

Now let us repeat the experiment with some Quantum marbles, these marbles have the property of not being a specific color until they are observed. Now if we repeat the experiment, what are the possible outcomes of a NOT blue observation, the ball we have must be red or yellow, if the ball is red the other can be yellow or blue, like wise if the ball is yellow the other can be red or blue. Note that there are now 4 possible outcomes, 2 of which are blue so there is a 50% chance of a blue result.

This difference in probability of the outcome is the Bell inequality.

Note that an good description of this is in Schroedinger's Kittens: In search of Reality by John Gribbin

 

[Ghidrah]

Yes, I should have said "related states" rather than "identical states."

Claude Bile, I assume the other photon did not actually change state, but that its superposition of states was collapsed to a single state. So the "spookiness" is actually that somehow the particle switches from a superposition to a single state. Thus, an experiment that gives different results for a superposed particle versus a non superposed particle can be performed, and, depending on whether the entangled photon has been observed or not, the outcome of the experiment on the OTHER photon actually changes. Or at least that's my current interpretation...

Integral, thanks for the book reference. I'll go dig it up. Your quantum marble model is thought provoking, and I see clearly the difference in measurement that results. How far can I take that model?

 

[Mk]

Welcome to physicsforums, Ghidrah!

Physicists entangle electrons by shining laser light on it. How does this work? Do they shoot it at both electrons at the same time and hope they entangle? Do they fetch already naturally entagled particles? How do they quantum teleport particles? How do they entangle photons?

 

[Claude Bile]

One method to entangle photons is using an Optical Parametric Oscillator. An OPO generates two frequencies (w1, w2) from a single pump frequency, whereby the sum of the two frequencies equals the pump frequency.

Now, obviously there are many combinations of w1 and w2 that satisfy this condition, however there is another condition called the phase matching condition, which basically boils down to conservation of momentum. For a specific angle of propagation, only up to two frequencies are allowed.

Importantly, Type II Birefringent phase matching demands that the two output frequencies have orthogonal polarisations.

Now, consider the degenerate case where w1 = w2, the output frequency is half the pump, thus now there are two output photons of frequency w1 for every pump photon. The two output photons must still have different polarisations, even though they are indistinguishable, thus the photons become entangled. Measurement of one polarisation will force the second photon to adopt the orthogonal polarisation.

Entangled photons generated in this fashion are used for Quantum Cryptography.

Claude.

 

[Mk]

Ooooh, much thanks, but what is pump frequency?

 

[HallsofIvy]

The problem with the "bags and marbles" analogy is that, classically, a bag will have a specific number of marbles of each color even though you don't know what that is. In quantum physics, the quantum properties are not fixed until you look at them.

Let's assume that you have 10 black and 10 white marbles mixed together in a draw. Without looking at them you pick out 10 marbles and put in a bag and walk away with the bag. If quantum physics applied to the marbles, there would NOT be a specific number of white and black marbles in that bag until you looked! Let's say you look and find there are 6 white and 4 black marbles. Quantum physically speaking before that moment, "black and white" was mixed among the marbles and the only "became" 6 white and 4 black when you looked (for some reason quantum physicists don't find that "spooky"!). Now, at that instant the 10 marbles you left back in your dresser draw must become 4 black and 6 white. THAT'S spooky!

 

[Claude Bile]

Ooooh, much thanks, but what is pump frequency?

The pump frequency is the frequency of the incident light. For example, if I pump an OPO with 532 nm (Green) light, I will get two 1064 nm photons for each 532 nm photon (In the degenerate case where w1 = w2).

Claude.

 

[nrqed]

One method to entangle photons is using an Optical Parametric Oscillator. An OPO generates two frequencies (w1, w2) from a single pump frequency, whereby the sum of the two frequencies equals the pump frequency.

Now, obviously there are many combinations of w1 and w2 that satisfy this condition, however there is another condition called the phase matching condition, which basically boils down to conservation of momentum. For a specific angle of propagation, only up to two frequencies are allowed.

Importantly, Type II Birefringent phase matching demands that the two output frequencies have orthogonal polarisations.

Now, consider the degenerate case where w1 = w2, the output frequency is half the pump, thus now there are two output photons of frequency w1 for every pump photon. The two output photons must still have different polarisations, even though they are indistinguishable, thus the photons become entangled. Measurement of one polarisation will force the second photon to adopt the orthogonal polarisation.

Entangled photons generated in this fashion are used for Quantum Cryptography.

Claude.

Very interesting. Thanks for your post.

I'm wondering: is there a well established theory behind the process leading to the production of the two photons? I mean is it a simple question of exciting atoms to a specific configuration that then cascades down emitting two photons correlated in their energy and polarizations? Or, as your comments seem to imply, it's rather a many-body effect where collective behavior of the atoms is crucial? In the latter case, is there an established theory or is it a property that was first observed experimentally and that has never been completely understood theoretically ? I've read somewhere that the physics behind all this was not completely understood, but it was a semi-popular description so I don't know if it's a reliable source.

Thanks again

Pat

 

[Claude Bile]

If you apply the correct electric field, the atom will become polarised in the correct way as to emit two photons.

The only prerequisite to this process occurring is that the response of the atom to an applied electric field is nonlinear (and assymetric in the case of 2nd order nonlinear processes), and phase matching requirements are met.

Phase matching ensures that, in a bulk medium, all the emitted photons are emitted in phase with one another. This condition is equivalent to conservation of momentum.

The fact that there are many atoms is not at all crucial, however it is normally necessary for an atom to be in a bulk media, such as a crystal to have the appropriate (i.e. nonlinear) response to an applied field. Also, in most NLO applications, we are concerned with macroscopic quantities, which is why the theory tends to be semi-classical.

Nonlinear effects were first observed after lasers were invented,as only lasers produce energy densities high enough for nonlinear effects to manifest themselves.

Claude.