# Entangled Particles and the Hadron Collider?

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1. Oct 28, 2014

### KooperScooper

If one was to entangle two particles and either send the two particles at each other, or send one of the entangled particles and observe the other; what do you think might happen?
If there are any problems with getting an entangled particle into the Hadron Collider, please say so.

2. Oct 28, 2014

### StevieTNZ

You say "send one of the entangled particles", but where are you sending that particle? Perhaps you can clarify.

3. Oct 28, 2014

### Staff: Mentor

Entangled in which way?
Neglecting some technical issues: you could send them in, but no matter how they are entangled, accelerating them in a particle accelerator would make them lose their entanglement quickly.

If you let two entangled particles collide at high energy, nothing special happens (again independent on the details). You get nothing you won't see in other collisions as well.

4. Oct 28, 2014

### Strilanc

Is that because the collision process effectively measures the spins, or because the collision outcomes don't depend on the spins, or some other reason?

For example, suppose that one of the possible collision outcomes is phased 180 degrees if the spin is up instead of down (but otherwise the collision doesn't depend on the spins). Then you would expect to never detect that phased outcome, because the two halves of the entangled state destructively interference on it. Where does that example fall apart?

5. Oct 28, 2014

### Staff: Mentor

Phased 180% relative to what? Destructive interference only occurs with superposition's of the same particle - leaving aside the issue of bosons and fermions. Two different particles, in general, do not destructively interfere.

Reading popularisations doest convey what entanglement really is.

Given an object that can be in two states |a> and |b> then if object 1 is in state |a> and object 2 state |b> that is written as state |a>|b>. Conversely if object 1 is in state |b> and object 2 in state |a> that is written as |b>|a>. But the superposition principle implies it can also be in a superposition of those states ie 1/root 2 |a>|b> + 1/root 2 |b>|a>. Since |a> and |b> are two different states there is no way for them to destructively interfere. Now if they were the same state - then you get the interesting effects of bosons and fermions you can read up about.

Analysing collision processes is often done with the aid of the so called S matrix:
http://en.wikipedia.org/wiki/S-matrix

Thanks
Bill

Last edited: Oct 28, 2014
6. Oct 29, 2014

### Strilanc

Phased 180 degrees as in a Z gate controlled by the spin being applied. The phase of the parts of the superpositions where the entangled spin is up get multiplied by -1.

Two particle systems can undergo interference. The particles won't cancel each other out, since that would violate unitarity, but you can set up experiments where multiple paths destructively interfering prevent the pair from appearing in certain positions just as you can with a single particle.

My understanding of entanglement doesn't come from pop science, it's from https://www.amazon.com/Quantum-Computation-Information-Cambridge-Sciences/dp/0521635039. Basically I know some of the linear algebra parts but very little of the differential equation parts.

For example, I'm thinking of the two particle system as a two-or-more qubit system. I know I can do multi-qubit interference things, like superdense coding and pseudotelepathy (awful name for a type of bell inequality), so the same should be true of particles.

Right, what I'm asking is if the collision process involves operations that send states to multiple outputs, and if the two states that are entangled might have overlapping outputs from those operations, and this would interfere. Like, if collision happens to do something isomoorphic to running part of the state through a Hadamard gate.

That's... going to take a while to digest.

Last edited by a moderator: May 7, 2017
7. Oct 29, 2014

### Staff: Mentor

Then you can see from the math if they are different states entanglement doesn't create destructive interference. Only if the states are the same can such occur - and that's how you get things like the Pauli Exclusion principle for Fermions.

I don't know why you keep mentioning spins - spins usually have nothing to do with particle collisions - but I have to say its not an area I am personally into. For sure though particle collisions do not measure spin in general.

Indeed. You might like to study QFT it forms part of. I am going through the following book right now and am pretty impressed:

Thanks
Bill

Last edited by a moderator: May 7, 2017
8. Oct 30, 2014

### Staff: Mentor

High-energetic collisions with hadrons are nearly independent of spin, as the collisions happen between partons within and you cannot control their spin anyway.

For electron-positron collisions spin is important, but there are just two options for the relative alignment. And you can control that with polarized beams as well, no need to have entangled particles.

9. Nov 4, 2014

### Strilanc

Thanks.

I'm surprised you can't do anything interesting by entangling the colliding particles into 1/sqrt(2) (|alignments-agree> + fun-phase-factor |alignments-disagree>).