Question about Entanglement and electron spin

[QuantumVegan]

I'm working on a research paper on Quantum Entanglement and came across something I don't understand. (I assume this goes here rather than in the homework forum because it applies to a topic rather than a problem. Sorry if I'm mistaken.) From what I've read, if two electrons are entangled, one will have an up-spin and the other will have a down-spin. However, there can be more than two electrons entangled (scientists have entangled three). With three electrons, there can't be just one with up-spin and one with down-spin, so what happens?
Secondly, what happens if two electrons with the same spin are entangled? For example, two electrons, each with up-spin, are entangled--one should stay up-spin and one should switch to down-spin, correct? Yet if they are entangled and have negligible differences, there is nothing to determine which one switches to down-spin and which one remains up-spin. How does this work?
Sorry if these are stupid questions, I am in 11th grade in high school so I have not yet had any quantum mechanics courses.

Any help is appreciated. Thanks.

 

[DrChinese]

Welcome to PhysicsForums, QuantumVegan!

The actual underlying rules are a) that there is conservation of spin; and b) the Heisenberg Uncertainty Principle applies - preventing you from knowing non-commuting spin components. An electron has 3 spin components: x, y and z (corresponding to 3D). None of these commute, so knowledge of Y means X and Z are completely uncertain.

If there are 3 entangled electrons (by convention electron spin is either +1/2 or -1/2), then spin will not total 0 as you say. It will be +1/2 or -1/2. I am not sure if the +3/2 or -3/2 entangled states are possible, I would guess so.

 

[QuantumVegan]

Thanks for the help! Yet I'm still wondering about one thing. Can two electrons with the same spin components be entangled, seeing as there is nothing to determine which one changes spin? Does this go by the assumption that the spin components do not exist until observed?

One other thing: It is required that the total of all spin components (x1+y1+z1+x2+y2+z2, with 1 and 2 denoting separate electrons) have a sum of 0, correct? How I understand it is then adding a third electron (or having any odd number of electrons) will violate this rule?

Thanks.

 

[zonde]

It seems that you are confusing two different things - Pauli exclusion principle and entanglement.
For electrons in a single atom, Pauli exclusion principle states that no two electrons can have the same quantum numbers.
Entanglement describes situation when describing two (or more) distant particles with single wavefunction gives you additional information about particles. Entanglement itself does not restrict how particles are entangled - with the same spin superposition or opposite.
Because of Pauli exclusion principle it might be hard to come up with mechanism for source producing three entangled electrons but that is not restriction of entanglement.

 

[QuantumVegan]

Sorry for the late response, I was busy with school and forgot about this.
I know what exclusion is; I read that entanglement requires opposite spins, but maybe what I read was mistaken. How I understand it now, two entangled electrons can each have +1/2, each have -1/2, or one of each, i.e., there is no restriction? Thanks.

 

[DrChinese]

Sorry for the late response, I was busy with school and forgot about this.
I know what exclusion is; I read that entanglement requires opposite spins, but maybe what I read was mistaken. How I understand it now, two entangled electrons can each have +1/2, each have -1/2, or one of each, i.e., there is no restriction? Thanks.

There are a number of ways to have entanglement, electrons with opposite spins are just one example. You can have photons, ions, etc. as well as partial entanglement or entanglement of "odd" observables. The point being that you have to look at specific situations.

So you are asking about 2 electrons, but it seems that you might have another underlying question. If so, you could share that and maybe learn a little more.

 

[QuantumVegan]

I know various things can be entangled; my question is specifically about electrons. Right now I am wondering: If exactly two electrons are entangled, do they necessarily have opposite spins?

 

[DrChinese]

I know various things can be entangled; my question is specifically about electrons. Right now I am wondering: If exactly two electrons are entangled, do they necessarily have opposite spins?

As far as I know, 2 entangled electrons always have opposite spins as you suggest. However, there are cases in which 3 or more electrons can be entangled and such will not always be the case. Of course, we are moving into some exotic setups in these cases. See for example:

http://arxiv.org/abs/cond-mat/0406672

 

[QuantumVegan]

Okay, thanks. Does that mean that it is impossible for a human to entangle exactly two electrons which initially (before entanglement) have the same spin?
If it is possible, is it random which electron will switch spin?