# Eigenvalues of entanglement

1. Mar 4, 2015

### lucas_

Lets' say you have an entangled pair of electrons with spin up and spin down. What is its eigenvalues.. is it..

Eigenvalue 1: Electron A with spin up
Eigenvalue 2: Electron A with spin down
Eigenvalue 3: Electron B with spin up
Eigenvalue 4: Electron B with spin down

But it's supposed to be entangled.. how come during measurement you don't get eigenvalues of..

Eigenvalue 1: Electron A + Electron B spin up
Eigenvalue 1: Electron A + Electron B spin down
?

2. Mar 4, 2015

### Jazzdude

You're confusing eigenstates with eigenvalues. And you don't specify which operator they are supposed to belong to.

3. Mar 4, 2015

### lucas_

Hamiltonian operators on position and spin. I want to understand the quantum state of entangled system versus unentangled system. In entangled system, the quantum state doesn't just contain particle A or particle B but they are entangled.. yet when you measured them.. they are in particle A or B.. so how do they differ when end results in the same.. are you saying that they have similar eigenvalues yet the eigenstates differ?

4. Mar 4, 2015

### Jazzdude

No, I'm not saying anything besides that your question is (still) not well formed. What Hamiltonian exactly? Your confusion seems to be much deeper than you believe, as you seem to not understand how these things relate at all.

5. Mar 4, 2015

### lucas_

In entangled system of particle A and particle B, the quantum state doesn't contain just particle A and particle B but their combination.
In the case of a photon or electron in a double slit experiment, the photon quantum state contain path A or B.. so they are not entangled.
In quantum mechanics.. how are analysis of entangled and unentangled system differ? what subtopics do they fall under. They seem to have similar projection or eigenvalues.

6. Mar 4, 2015

### Jazzdude

Again, what is your Hamiltonian? If you ask for eigenvalues and eigenstates of the Hamiltonian, you have to specify it.

7. Mar 4, 2015

### lucas_

oh sorry not the Hamiltonian, but the position operator. In the entangled pair, how is its position operation differ to that of an unentangled pair? In the entangled pair, particle A and particle B are mixed.. so when performing the position operator, how come you still get the position of particle A and not their combined state?

btw.. what is the operator for spin?

8. Mar 4, 2015

### Jazzdude

The position operator only acts on a single particle state space. Its eigenstates are therefore the same as in the single particle case.

9. Mar 4, 2015

### lucas_

Thanks. What other operators only act on a single particle state space beside the position operator?