Entanglement: Behaviour of Particles & Real Life Apps

[Andyhs]

TL;DR Summary

Entanglement query

1) Entanglement is about the behaviour of a particle can be determined by measurement of the behaviour of another particle.
At some website, it explains that the reason behind is due to conservation of momentum. When a particle is split into two particles (say particle A and particle B), the total momentum of the particles should be same as the momentum of the original particle.
My query is when we measure the status of such a small particle (say particle A), the momentum of the particle A should be affected.
Then, how can we conclude the status of particle B ?

2) In real time life application of Entanglement (say for encrypted communication), how can we make two particles which are far in distance be entangled ?

 

[PeroK]

Summary:: Entanglement query

My query is when we measure the status of such a small particle (say particle A), the momentum of the particle A should be affected.
Then, how can we conclude the status of particle B ?

Conservation of momentum is one law of nature that can put two particles into an entangled state, both classically and in quantum mechanics. Generally, the two particles must have equal and opposite momentum.

If you measure the momentum of particle A, then in principle that tells you the momentum of particle B. It doesn't matter whether you let particle A crash into something and measure its momentum that way. The change to particle A does not affect particle B.

In QM measuring momentum gets a bit messy conceptually. It's not so clear cut as measurements of quantum spin or photon polarisation.

Summary:: Entanglement query

2) In real time life application of Entanglement (say for encrypted communication), how can we make two particles which are far in distance be entangled ?

The entanglement is generally created during some process where the two particles are together. They are then separated and sent off in different directions, but the entanglement remains.

Here's a crude analogy: You take a pair of shoes, put each in a box and send them off to different people. The shoes are "entangled" in the sense that one is left and one is right. That's the basic idea.

 

[Andyhs]

Thanks for your reply.

Q1) As your reply, It doesn't matter that the status of Particle A is changed during observation as we have already observed the status of particle A.
Does it mean in real life application, we have to create entangled particles continuously as the previous pair of particles can be reused after observation ?


Q2) As your reply, the entangled particles are usually created in the same place and then send to different locations.
(a) When the entangled particles are sent to different places, will the momentum of the particles be changed due to external environment effect / the intended force applied while sending them ?
(b) For long distance communication, how is it realistic to create entangled particles and send them to different locations which are far away ?

 

[PeroK]

Q1) As your reply, It doesn't matter that the status of Particle A is changed during observation as we have already observed the status of particle A.
Does it mean in real life application, we have to create entangled particles continuously as the previous pair of particles can be reused after observation ?

Any measurement on an entangled state breaks the entanglement. Particles only stay entangled until they are measured.

If you have two objects moving with equal and opposite momentum (perhaps because they exploded from the same source) and you stop one object, the other doesn't stop!

Q2) As your reply, the entangled particles are usually created in the same place and then send to different locations.
(a) When the entangled particles are sent to different places, will the momentum of the particles be changed due to external environment effect / the intended force applied while sending them ?
(b) For long distance communication, how is it realistic to create entangled particles and send them to different locations which are far away ?

Momentum can't be used as a reliable quantity for communication. Generally you would use spin or polarisation. What you want is something that has only binary values when measured.

In terms of practical quantum encryption systems, you can research that yourself. Like any communication system you may get some "noise" or disturbance. Conventional networks have "parity" bits and other features to detect message loss or corruption. Quantum encryption systems, I imagine, are no different. In theory, however, the state of a system is not changed until measured.

 

[Dali]

Before going into the details, let's get the basics right:

1) Entanglement is about the behaviour of a particle can be determined by measurement of the behaviour of another particle.

Not really. Many popular explanations mix up entanglement with plain correlation. It is true that all entangled pairs of particle are correlated, but not the other way around, i.e. all correlated pairs are not entangled. Entanglement is a very special and very strange type of correlation!
The crude examples of pairs with a known total momentum, or shoes in separate boxes, are really only examples of correlation:

Here's a crude analogy: You take a pair of shoes, put each in a box and send them off to different people. The shoes are "entangled" in the sense that one is left and one is right. That's the basic idea.

There is really nothing interesting going on between two shoeboxes just from the fact that their contents are correlated. Opening one box tells us what is in the other, but does not affect the other in any way.

Now, (quantum) entanglement is a strange phenomena that occurs in some special cases where two (or more) particles are set in a state were their combined wavefunction can not be written as a product of single-particle states. That means that a measurement on one of the particles alters the wavefunction of the other. So a more correct definition of entanglement in your terminology could be:

1) Entanglement is when the choice of measurement on one particle has an impact on the outcome of measurements of another particle.

This is a strange type of correlation indeed! At first it seems like it would violate locality directly by necessarily sending information about the first measurement to the other particle (that might be very very far away). Or that you could use it to transmit information faster than light from A to B by choosing to measure or not at particle A, and then detecting some change on particle B (far away). But in quantum entanglement the effect on the other particle is never observable by measuring it alone. Only when combining and comparing the results of the two measurements can you see that their mutual correlation is such that one measurement must have affected the other.

 

[PeroK]

That means that a measurement on one of the particles alters the wavefunction of the other. So a more correct definition of entanglement in your terminology could be:

1) Entanglement is when the choice of measurement on one particle has an impact on the outcome of measurements of another particle.

This is inaccurate. For entanglement, there is a single two-particle state. Each particle does not have its own wavefunction.

The choice of measurement of one particle does not impact the outcome of a measurement of the other. In the sense that:

1) Do not measure particle A and perform a measurement on particle B. Repeat this process many times (for entangled pairs A and B) and record the results for particle B.

2) Perform a measurement on particle A and then perform a measurement on particle B. Again, repeat and record the results for particle B.

The results for particle B are the same in each of the cases 1) and 2). There is no way to tell by looking at the results for particle B, whether any measurement of particle A has taken place.

 

[Dali]

This is inaccurate. For entanglement, there is a single two-particle state. Each particle does not have its own wavefunction.

The choice of measurement of one particle does not impact the outcome of a measurement of the other. In the sense that:

1) Do not measure particle A and perform a measurement on particle B. Repeat this process many times (for entangled pairs A and B) and record the results for particle B.

2) Perform a measurement on particle A and then perform a measurement on particle B. Again, repeat and record the results for particle B.

The results for particle B are the same in each of the cases 1) and 2). There is no way to tell by looking at the results for particle B, whether any measurement of particle A has taken place.

That is what I tried to say in simpler words. I agree the wording "affecting the wavefuntion of the other" is too simplified for a two-particle state. But clearly a measurement of one of the particles affects the whole two-state wavefunction (that the other particle is a part of). And the fact remains that when you compare the two results (i.e. measure their correlation), the measured correlations are incompatible with the assumption that the measurements are independent. In simpler words that means measurement of A in some way must affect the result of B. Even though, as we both say, there is no way to know that by measuring B alone.

 

[PeroK]

In simpler words that means measurement of A in some way must affect the result of B. Even though, as we both say, there is no way to know that by measuring B alone.

That's a realist interpretation of the correlation. There is no result for B to be affected. The result for B is correlated with the result for A. That's all you can say.

As you probably know, you can perform this experiment where the measurement events are spacelike separated. In that case, which measurement came first, hence which measurement "affected" the other, becomes frame dependent.

 

[Dali]

That's a realist interpretation of the correlation. There is no result for B to be affected. The result for B is correlated with the result for A. That's all you can say.

Actually, you can say more. They are correlated in a specific way that would have been impossible if the two measurements were independent of each other. That is the assumption of separating variables in the derivation of Bell's inequality that is violated here. And not violated for correlated shoeboxes.

Entanglement is more than mere correlation. That is what I was trying to explain in simpler terms to the OP.

 

[PeroK]

Actually, you can say more. They are correlated in a specific way that would have been impossible if the two measurements were independent of each other. That is the assumption of separating variables in the derivation of Bell's inequality that is violated here. And not violated for correlated shoeboxes.

Entanglement is more than mere correlation. That is what I was trying to explain in simpler terms to the OP.

The assumption of Bell's theorem is that the measurements are governed by hidden variables, obeying the laws of probability. They are not independent in the statistical sense.

The assumption of QM is that the measurements are governed by complex probability amplitudes, which in certain cases achieve a correlation that is impossible using hidden variables.

 

[Dali]

The assumption of Bell's theorem is that the measurements are governed by hidden variables, obeying the laws of probability. They are not independent in the statistical sense.

The assumption of QM is that the measurements are governed by complex probability amplitudes, which in certain cases achieve a correlation that is impossible using hidden variables.

You keep missing out on some of the complexity here. There are TWO basic assumptions that go into the derivation of Bell's inequality; hidden variables (Objectivity), and separation of variables in the correlation function, corresponding to the assumption that the measurements are independent (Locality). That is why measured violation of the Bell inequality is said to rule out all Objective Local Theories (OLT's).

So, yes, if I take a realist's view I must conclude that the Bell experiments violate locality. If I instead want to keep locality I must give up objectivity. The experiments can't tell which interpretation is the correct one. Only that the world can't be both objective and local.

(The most common interpretation in these cases is usually the realist case, were locality seems violated. But one can equally follow a strict Copenhagen or non-realist interpretation and claim that before we have brought the results of the two measurements together into one single place and compared them, we have not yet measured the correlation. So we can't claim it exists before then. And the world(s) of all possible outcomes are still equally real before that point. In the many worlds theory that corresponds to worlds splitting with observers in all possible outcomes, and only at the time of actual comparing the results certain worlds are split away from each other. Nothing is non-local in that interpretation. But instead explicitly non-objective.)

 

[PeroK]

You keep missing out on some of the complexity here.

There is no complexity unless you go looking for it. The measurement outcomes are correlated, according to the original two-particle wavefunction.

It's only when you try to explain in realist or causal terms how nature achieves this correlation that the difficulties arise. Not that I'm especially advocating avoiding that question!