Wednesday, April 22, 2015

Quantum Entanglement For Dummies

Over the years, I've given many references and resources on quantum entanglement on this blog (check here for one of the more comprehensive references). Now, obviously, many of these sources are highly sophisticated and not really meant for the general public. It is also true that I continue to get and to see question on quantum entanglement from the public. Worse still, the Deepak Chopras of the world, who clearly do not understand the physics involved, are bastardizing this phenomenon in ridiculous fashion. But the final straw that compelled me to write up this thing is the episode of "Marvel Agent of Shield" from last night where the top brass of HYDRA was trying to explain to Bakshi what "quantum entanglement" is and how Gordon was using it to teleport from one location to another. ABSURD!

So while this is all brought about by a TV series, it is more of a reflection on how so many people are really missing the understanding of this phenomenon. So I intend to explain this is very simple language and using highly-simplified picture to explain what quantum entanglement is. Hopefully, it will diminish some of the false ideas and myth of what it is.

Before I dive into the quantum aspect of it, I want to start with something that is well-known, and something we teach even high school students in basic physics. It is the conservation of momentum. In Figure 1, I am showing a straight-foward example of conservation of linear momentum case, a common problem that we give to intro physics students.


In (a), you have an object with no initial linear momentum. In (b), it spontaneously splits into two different masses, m1 and m2, and go off in opposite directions. In (c), m1 reaches Bob and m2 reaches Alice. Bob measures the momentum of m1 to be p1.. Now, this is crucial. IMMEDIATELY, without even asking Alice, Bob knows unambiguously the momentum of m2 to be p2 simply via the conservation of linear momentum. He knows this instantaneously, meaning the momentum of m2 is unambiguously determined, no matter how far m2 is from Bob. When Alice finally measures the momentum of m2, she will find that it is, indeed, equal to p2.

Yet, in all the years that we learn classical physics, never once do we ever consider that m1 and m2 are "entangled". No mystical and metaphysical essays were ever written about how these two are somehow connected and can "talk" to each other at speeds faster than light.

Now, let's go to the quantum case. Similar scenario, outlined in Figure 2.


Here, we are starting to see something slightly different. We start with an object with no net spin in (a). Then it spontaneously splits into two particles. This is where it will be different than the classical case in Figure 1. Each of the daughter particles has a superposition of two possible spin states: up and down. This is what we call the SUPERPOSITION phenomenon. It was what prompted the infamous Schrodinger Cat thought experiment where the cat is both alive and dead. This is crucial to understand because it means that the state of each of the daughter particle is NOT DETERMINED. Standard QM interpretation says that the particle has no definite spin direction, and that until it is measured, both spin states are there!

Now, when one daughter particle reaches Bob, he then measures it spin. ONLY THEN will the particle be in a particular spin state (i.e. the commonly-described as wavefunction collapsing into a particular value). In my illustration, Bob see that it is in a spin-down state. Immediately, the spin state of other particle at Alice is in the spin-up state to preserve the conservation of spin angular momentum. When Bob measures the pin of his particle, he immediately knows the spin of the particle at Alice because he knows what it should be to conserve spin. This is similar to the classical case!

This superposition of state is what makes this different than the above classical example. In the classical case, even before Bob and Alice measure the momentum of their particles, there is no question that the particles have definite momenta all through its trajectory. Classical physics says that the momentum of each particle are already determined, we just need to measure them.

But in quantum physics, this isn't true. The superposition principle clearly has shown that in the creation of each of those two particles, the spin state are not determined, and that both possible states are present simultaneously. The spin state is only determined once a measurement is made on ONE of the particles. When that occurs, then the spin state of the other particle is also unambiguously determined.

This is why people have been asking how the other particle at Alice somehow knew the proper spin state to be in, because presumably, before any measurement is made, they both can randomly select either spin state to be in. Was there any signal sent from Bob's particle to Alice's to tell it what spin state to be in? We have found no such signal, and if there is, it has been shown that it will have to travel significantly faster than c. No matter how far apart the two daughter particles are, they somehow will know just what state to be in once one of them is measured.

This, boys and girls, is what we called quantum entanglement. The property of the quantum particles that we call "spin" is entangled between these two particles. Once the value of the spin of one particle is determined, it automatically forces the other particles to be in a corresponding state to preserve the conservation law.

But note that what is entangled is the property of the particle. It is the information about the property (spin) that is undergoing the so-called quantum teleportation. The particle itself did not get "teleported" the way they teleport things in Star Trek movies/TV series. It is the property, the information about the object, that is entangled, not the entire object itself. So in this example, the object doesn't jump around all over the place.

The physics and mathematics that describe quantum entanglement are more involved than this cartoon description, of course. There are mathematical rules resulting in physical constraints to the states and properties that are entangled. So you just can't pick up anything and say that you want to entangle it with something else. It just doesn't work that way, especially if you want to clearly observe the effects of the entanglement.

The important lesson to take away from this is that you can't learn physics in bits and pieces. If you simply focus on the "entanglement" aspect and are oblivious to understanding the existence of quantum superposition, then you will never understand why this is very different and mysterious than the classical case. In physics, it is not uncommon that you have to also understand a series of things leading up to it. This is why it is truly a knowledge and not just merely a series of disconnected information.

Zz.

17 comments:

Peter Morgan said...

You gloss the preparation aspect a little, in that Bob only knows p2 in the classical case because he knows that (b) is consistently prepared from a zero momentum state, not sometimes starting with something moving, which we have checked to be true by comparing Alice's and Bob's results in the past. Without some reference to the past, Bob can predict nothing about what has or will happen elsewhere (with the usual hope that the preparer doesn't go for a cup of tea at an inopportune moment, or fall against the apparatus, there's an earthquake, etc.).

In the quantum case there is exactly the same proviso, that the preparation must be consistent, albeit in the quantum case the preparation is always stochastic. Given that we know what Alice and Bob have observed in the past —we've checked the source— we can predict the probabilities of what we will see next time better than if we didn't know what the source might be, and if we've seen our own result we can make a better guess what Alice will see/have seen.

Taking it that we have thought about the Bell experiments, there are several moves we can use to make them seem more classical: we can introduce some kind of incoherent nonlocal dynamics that we can't control, at least not well enough for us to be able to send messages; we can say that the statistics are as we see them just because the initial conditions in the past were what they had to be for us to see what we see now (not impossible, just very unlikely - the Sherlock Homes maneuver); we can introduce a many worlds approach (though perhaps that's only close to classical); insert your favorite, if any. Alternatively, it's a brute empirical set of facts that things are this way.

Your quantum mechanical account has an unfortunate starting point. "We start with an object with no net spin in (a)", presupposing that there is "an object". OK, particle physicists talk this way all the time, but it cuts off almost a hundred years deliberation about whether there is or isn't a particle. Yes, there are events in our detectors, and we know ways to change the statistics of events in our detectors, without being able to control individual events, but are there objects that go from one place to another to make those changes happen? Art Hobson, to whose work you introduced me quite a few years ago, goes some way to constructing a way of thinking about this stuff in terms of fields; though I've pretty much decided that classical his approach is not, nonetheless it at least gives some kind of alternative to talking about objects.

raduray said...

Thank you for the dumbed down explanation. Very useful for a non-physicist like me. But here's a question: If Bob were to changed the spin direction of his particle, would Alice's particle also change direction? I suspect not, since Bob would have to apply energy to change his particle's spin and that would probably break the entanglement. If yes, however, then we have a theoretical path to faster than light communication.

ZapperZ said...

If Bob does that, then the entanglement with the first particle is now lost, because an external factor has changed its state.

Remember that all the detector does is to measure the state of the particle. It doesn't impose anything onto the particle other than to coax it to reveal itself.

Zz.

raduray said...

Another newbie question. How do we prove that the spin of the particles is undetermined until when it is observed? Maybe it was determined at separation and the observation only confirmed its status.

ZapperZ said...

Ah, then you are questioning the validity of the concept of superposition in QM. This is the issue that has been dealt with when we talked about the Schrodinger Cat-states.

There are already many physical evidence for this, especially in Chemistry. In fact, many well-known observations in Chemistry existed way before QM was formulated. It is only after QM that we now have a clear explanation or description on what they were seeing in Chemistry.

This is on top of the many new experimental evidence, such as the Stony Brook/Delft's SQUID experiments that clearly shows the effect of the presence of such superposition.

You should also do a search in this Blog on the concept of "Realism". I had just posted an entry on the death of "Local Realism", which is a classical concept that you had described.

Zz.

Greg Marsters said...

Does the loss of superposition by the photon reaching Alice result in any changes in what it can be used for? For example does it fail to create an interference pattern in a slit box? Though I guess that would transfer of information which is "not allowed". There needs to be some element of an easy explanation where the effect can only be detected when the two detectors bring their information together again.

Gabriel Edery said...

ZapperZ - I think you missed the point regarding "teleportation" and quantum entanglement.
I don't know you so I can't be certain, but I believe you know the phenomenon called "quantum teleportation" presented by Prof. Asher Peres among others. I short, it states that you can teleport an unknown state from one point to another using an entangled state shared in both points (the nice example of Alice and Bob) called a "Bell state". In practice, what is being teleported is the information of the particle - it's state. Quantum teleportation is a form of communication (very much like a fax, except that the original is destroyed - obeying the no-cloning theorem).
The whole idea of comparing quantum to fictional teleportation is that you could, theoretically, define the state of all particles of an object, disassemble it in one lab (the no-cloning theorem), teleport the states of the particles using a shared Bell state, and then assemble it in the other lab (as it was proved experimentally before with atoms).
So I think that the comparison is still admissible...
Anyway, very nice and concise explanation of a tricky phenomenon!

ZapperZ said...

So what exactly did I missed?

You stated that "in practice, what is being teleported is the information of the particle..."

What is the difference between that, and what I wrote:

"But note that what is entangled is the property of the particle. It is the information about the property (spin) that is undergoing the so-called quantum teleportation. The particle itself did not get "teleported" the way they teleport things in Star Trek movies/TV series. It is the property, the information about the object, that is entangled, not the entire object itself. So in this example, the object doesn't jump around all over the place."

You may teleport the states to another location, but you do not send matter over. It has to be replayed with matter that already exists at that distance location.

So no, I do not see the comparison between quantum teleportation and Star Trek teleportation to be admissible.

Zz.

Gabriel Edery said...

My statement that you quoted is analogous to yours. The difference between my idea and yours is stated in the last part of my comment: "The whole idea of comparing quantum to fictional teleportation is that you could, theoretically, define the state of all particles of an object, disassemble it in one lab (the no-cloning theorem), teleport the states of the particles using a shared Bell state, and then assemble it in the other lab (as it was proved experimentally before with atoms)".
You may redefine "classical" teleportation this way (very much like a fax and a 3D printer).

ZapperZ said...

Yes, and I fully understand and I addressed that. No "matter" was teleported. Only information. This is not a transportation of matter from one location to another. It is a transportation of information. The fax that you received is merely the image made at the origin, and then "replayed" onto a piece of a paper, with the paper already at the target location. The paper did not get transported.

That is my whole point.

"Redefining" classical teleportation in this way doesn't change anything. Accepting it or not accepting it is simply a matter of taste. It doesn't change the physics.

So how badly did I miss this so much so that you tell that I "missed the point"?

Zz.

Gabriel Edery said...

What I meant by "missing the point" was that you could (as you said, it's a matter of taste) understand classical teleportation using quantum teleportation. Maybe my phrasing was a little off and for that I'm sorry (English is not my native language). Evidently, we are both saying the exact same thing - quantum teleportation is the teleportation of information and not matter. I just gave a way (physically possible) to explain classical teleportation

Unknown said...

How does a quantum computer use this to instantly transfer information? Also, how does it instantly transfer data? It sounds like our knowledge of the universe is flawed.

ZapperZ said...

Dear Unknown,

How in the world did you go from "How does a quantum computer use this to instantly transfer information? Also, how does it instantly transfer data?" to concluding that our "knowledge of the universe is flawed"? If there's anything that's flawed here, it is YOUR sequence of logic.

Zz.

treesd said...

Thanks for explaining this, but I still do not get the point of it, I mean, bob knows what alice will know, right?, so... how does this make it faster in any way?, if alice cannot know, if bob does not tell her or till she get it herself, or maybe I am missing the point?.

P.D. English is not my native language.

Louis Apostolakis said...

Would the following analogy work?

You "entangle" two pennies. You spin each penny on a table. At some random point in time, you slap the one penny down and observe it as heads or tail. At that instant, the other penny falls flat with the opposite side up.

Billz said...

When measuring entangled spin as in your figure 2, do the measurements performed by Alice and Bob have to done simultaneously? Say Alice performs her measurement at a later time than Bob. Will those non-simultaneous measurements still show particle entanglement?

Darrall Blanchet said...

I'm not sure that I am looking at your illustration correctly but isn't the down arrow at Bob's particle indicating a counterclockwise spin? If so isn't the down arrow at Alice's particle indicating the same spin?