Quantum Entanglement

[Anonymous No.4954161]

I've taken QM courses, but I never learned about quantum entanglement. What I know is only from pop-sci articles.

Basically, when two entangled particles are created if one is in a certain state then at that exact moment the other particle is necessarily in the opposite state, almost as if they were communicating with one another.

Discussion of this topic in the realm of pop-sci is often accompanied by talk about violation of relativistic causality. However, I don't see why any sort of connection would be required to explain this phenomena. For example, if you put egg timers set to the same time in two cars they would go off at the same time, without any communication between the two.

[Anonymous No.4954171]

If quantum entanglement was real, you could send information faster than light.
Think of it this way: Two people are each given two cards and then they move away from each other. When person A chooses one of his cards then, the duplicate of that card instantly disappears at person B's place. Instant transmission of information.

[Anonymous No.4954173]

From the one book I've read, the example given was two photons being emitted from the same source at the same time, with opposite polarization.

The path an individual photon will take through a polarizer is probabilistic, yet the two photons will always take different paths through polarizers of the same orientation. Bell's inequality rules out any hidden variables, so it seems that information is being exchanged between the two photons instantaneously.

You probably know more about this than me, to be honest.

[Anonymous No.4954174]

Watch this
http://www.youtube.com/watch?v=0Eeuqh9QfNI&feature=BFa&list=PLF049C87F35C3A8D3

[Anonymous No.4954180]

In quantum mechanics, a pure state is a vector in a Hilbert space. A state of a compound physical system, because of the way CP(n) works, cannot come from a pair of states in two subsystems, instead there is a sum of each. There is no combination of individual basis states, unlike a product or mixed state which is factorable.

[Anonymous No.4954178]

your analogy with the egg-timers does not fit

[Anonymous No.4954190]

Eliezer Yudkowsky explains it pretty well in http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ .

[OrganicEuphoria !C5Eg6mdVac No.4954196]

>>4954161

Basically, quantum entanglement arises
due primarily to the tensor product structure of the Hilbert space and the linear superposition principle when you deal with multiparticle systems.

[OrganicEuphoria !C5Eg6mdVac No.4954203]

>>4954161

Basically, quantum entanglement arises due primarily to the tensor product structure of the Hilbert space and the linear superposition principle when you deal with multiparticle systems.

[OP No.4954209]

It's been over a year since I last studied QM. Looks like I have to dust off the old text book and relearn Bell's theorem.

[Anonymous No.4954214]

To illustrate what's "spooky" about entanglement, I'm going to tell a story about dragon eggs. In real life, you can do this stuff with entangled pairs of photons.

Dragons lay eggs in pairs. Some people claim the twin eggs have a special connection to each other. But we're just going to report the facts.

There are three experiments you can do with a dragon egg:

You can smash it and observe whether the yolk is red or green.
You can set it on fire and observe whether the flame is red or green.
Or you can wait for the dragon to hatch, and observe whether the baby dragon is red or green.

The trouble is that once you perform one of these experiments on an egg, it is impossible to do any of the others.

Twin dragon eggs are utterly useless for communication, at least in the ordinary sense. The probability of getting red when you do one of these experiments is always 50%, regardless of what is done to the other egg. They can be used in cryptography to give two parties a random bit which nobody else knows, but you can't send an actual message with them.

[Anonymous No.4954222]

The weirdness only shows up when you study the properties of the pairs. Let's start with a few facts:
* If you let one egg hatch and smash its twin, the probability of getting different colors is 25%.
* If you smash one egg and set one egg on fire, the probability of different colors is also 25%.
* And if you set one egg on fire and let the other hatch, the probability of different colors is again 25%.

We might make the following argument:
For the dragon from Egg 1 to have a different color from the dragon from Egg 2, one of the following must be true:
a) Dragon color 1 =/= Yolk color 2 (25% of cases)
b) Yolk color 2 =/= Flame color 1 (25% of cases)
c) Flame color 1 =/= Dragon color 2 (25% of cases)
Therefore the probability of the dragons having different colors is at most 75%.

But when the experiment is carried out and the twin dragons hatch, they have different colors 100% of the time.

[Anonymous No.4954233]

How far in quantum mechanics did you get? Do you know how to work with state vectors or did you just do single-particle wavefunctions like some courses start out with? Did you ever learn about spin? And what about product states?

[Anonymous No.4954236]

>>4954233
>product states
*tensor product states

[OP No.4954265]

>>4954233
I've taken QM I & II, but was never good at math, I haven't used QM in over a year, and I'm not sure I had a good grasp of it to begin with. I got an A and a B fair and square though so I guess I was doing something right.

[Anonymous No.4954277]

>>4954265
It's rather simple maths.

In a nutshell, if you have two subsystems, <span class="math">H_1 , H_2[/spoiler] which are both Hilbert spaces then <span class="math">H= H_1 \otimes H_2[/spoiler] necessarily implies the state is separable. Suppose you have a linear map <span class="math">h: H_1 \times H_2 \to H_1 \otimes H_2[/spoiler], then a state pair <span class="math">(\psi_1, \psi_2)[/spoiler] looks like <span class="math">\psi_1 \otimes \psi_2[/spoiler], which is seperable. By definition an entangled state cannot be written as <span class="math">\psi_1 \otimes \psi_2[/spoiler], instead it is a nontrivial sum of states from the two subsystems.

[Anonymous No.4954280]

>>4954265
>I & II
That doesn't tell us anything.
The real question is whether you would understand what something like <span class="math">|\uparrow\rangle \otimes |\downarrow\rangle[/spoiler] means and how to work with it.

[Anonymous No.4954291]

>>4954277
Are tensor products really introduced in QM I & II classes? Is there a point to this without a serious course in module theory?

I'm curious, computer science student myself, have not done physics.

[Anonymous No.4954300]

coursera has a course on quantum computation, which introduces entanglement

[Anonymous No.4954302]

>>4954291
Depends on what you mean by "QM I" and "QM II". This is sophomore level maths in my university for a physics major.

I don't understand how you can take a course in something, especially like QM, without having any clue what you're really doing.

Solving the Schrodinger equation for the hydrogen atom and doing elementary group theory for spin, i.e. QM "applications" is reserved for a course called "Quantum Mechanics for Engineers" where I'm at.

[Anonymous No.4954317]

>>4954302
Well in what way are tensor products defined in such a QM course? I found that tensor products are quite complicated, at least from an algebraic perspective.

[Anonymous No.4954331]

>>4954317
>Well in what way are tensor products defined in such a QM course?
They aren't defined. They are used without understanding what they are.

[Anonymous No.4954348]

>>4954317
They aren't defined, you need a separate course for that.

I was taught to treat the tensor product with monoidal categories.

[Anonymous No.4954358]

>>4954331
>>4954348
Uhh, sounds boring. But I guess one has to take things for granted when dealing with undergraduate physics. And yes, tensor product is a nice application of the categorical concept of universal property.

[Anonymous No.4954673]

magic