# What is conserved in the various forms/types of entanglement?

• San K
I would consider their spin entangled. I can't imagine anybody reading it that way.In summary, entanglement is the correlation of states between two unobserved entities that have interacted. This can occur in various ways, such as through spin, momentum, position, polarization, and other properties. The law of conservation of (angular) momentum can partially explain why spin entanglement occurs, while other properties may be entangled due to different laws. The joint state of entangled entities is not the tensor product of their individual states, and observation ends entanglement. Therefore, entanglement is a fundamental aspect of quantum mechanics and can apply to various properties of entities.

#### San K

What is conserved in the various "forms/types" of entanglement?

What law is applicable for each of the "entanglement factors"?

Particles can be entangled in various way/factors such as momentum, spin, polarization etc.

For spin entanglement we can say that:

The law of conservation of (angular) momentum explains (at least partially) why the spins must be correlated.

How about the other properties (on which a particle may be entangled), such as position or polarization etc? Which law would be applicable in each of the cases above?

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I think for position entanglement it would be "conservation of position"...sort of...

This question is a little strange and I'm not surprised you're getting no answers. I have never heard of "conservation of position" ;-).

Anyway, I think the best answer I can give is that when we study entangled particles, we typically do not want them interacting with anything else because that has the potential to screw up the delicately prepared entangled state. So in studies of entanglement we usually think of the system as "closed" so pretty much every conservation law holds.

Entanglement is simply that unobserved entities (with a superposition of states) have interacted and now have correlated states. Once one is measured, the other's options are limited (must correlate).

I'm not entirely sure what you are asking, but it seems to me that the laws of conservation doesn't quite enter the way you think it does.

San K said:
The law of conservation of (angular) momentum explains (at least partially) why the spins must be correlated.

Consider two different entangled states, |01>+|10> and |00>+|11>. If 0 and 1 is represented by spin down and spin up respectively, then you could say that the spin is conserved in the first case, since either situation finds the sum of 0 spin between the two particles. However, the second state is equally entangled, but here you either find both particles in spin up OR both in spin down, i.e. no conservation.

Of course, spin conservation must apply, but only to the full system, including whatever mechanism you used to create the entanglement (often photons).

I am surprised at many of the answers above especially those who seem surprised that position can be entangled.

Go back an read the original Einstein et al 1935 paper, the thought experiment is two quantum systems interacting in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta in the same direction.

The question isn't silly it is probing the question the OP hasn't worked out how to ask which is what fundamental properties of the universe can be entangled in other words he is asking superselection rules.

http://en.wikipedia.org/wiki/Superselection

The quick answer is spin, polarization, position, particle number and energy have been proved to exist in a quantum superposition.

AFAIK states of different charge, strangeness, charm, color theoretically can be superposed as they are defined as quanta but no observational proof but I will leave that to the experts.

Entanglement is simply that unobserved entities (with a superposition of states) have interacted and now have correlated states. Once one is measured, the other's options are limited (must correlate). I'm thinking that anything about the entity that can be affected by something else without it being an observation, can be entangled. Anything that causes correlated states. Obviously observation ends entanglement.

Entanglement

meBigGuy said:
Entanglement is simply that unobserved entities (with a superposition of states) have interacted and now have correlated states. Once one is measured, the other's options are limited (must correlate). I'm thinking that anything about the entity that can be affected by something else without it being an observation, can be entangled. Anything that causes correlated states. Obviously observation ends entanglement.

Entanglement is not that simple. The joint state of entangled entities is not the tensor product of the individual states. A pair of independent vertically polarized photons are correlated with state |vv⟩, but not entangled.

I guess I said it poorly. If they haven't affected each others spin, then they are not entangled with respect to spin. I was getting at the concept that if one unobserved quantity interacted with another unobserved quantity then the entities are entangled with respect to that quantity. The joint state is no longer a product state. If the quantities are independent then they are independent.

As Zafa Pi said but I will put it simpler for you ... you need two to tango with entanglement, superposition requires only one thing in two states.

I am going to use particle but I guess these days it should be particle /object/unit to allow for the fact that you can get macro object entanglement.

Before entanglement each particle is described by its own quantum state, but after conditioning to entangle the pair it can still be described with a definite quantum state but each member of the pair must also be described relative to one another.

I think that's what you are implying but just checking your statement as originally put could be something to do with superposition but you seem to clear that up above because you talk about each others spin.

I read your post the same way Zafa Pi did but probably a bit worse so sorry if this is old hat.

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I'll try to say it again. If two entities interact and affect each other in any way short of observation, the quantities (characteristics) that were affected are entangled. (if they were classical objects then there is no entanglement). I think that is what I said the first time. My point is that anything about a quantum entity becomes entangled if that "anything" is affected by another quantum entity (interaction). The two entities then have correlated values for that "anything".

The system is no longer represented by its pre-entanglement product state.

I think you have to read my first response in a pretty strange way to assume that I said that if two particles interacted in a way that didn't affect their spin, that I would consider their spin entangled.

BTW, I am not an expert, so correct me if I am wrong.

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I'm not sure if this fits in this thread, but as professor Michio Kaku explains, the quantum theory is messy. If you look at the quantum theory of these tiny objects, and compare it to theory of relativity of larger objects as starts, planets, galaxies etc. they do not fit together - they don't work under the same physical principles. That is a big problem. Therfor, he explains, the string theory will solve this. Link to a video: starts at approx 09:00

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