What Are the Eigenvalues of Entangled Electron Spins?

In summary, the conversation discusses the concept of entangled pairs of electrons and the difference between their eigenvalues and eigenstates. The conversation also mentions the Hamiltonian operator and its role in analyzing entangled and unentangled systems. It is clarified that the position operator only acts on a single particle state space and its eigenstates are the same in both entangled and unentangled pairs. The conversation concludes with a question about other operators that only act on a single particle state space.
  • #1
lucas_
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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
?
 
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  • #2
You're confusing eigenstates with eigenvalues. And you don't specify which operator they are supposed to belong to.
 
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  • #3
Jazzdude said:
You're confusing eigenstates with eigenvalues. And you don't specify which operator they are supposed to belong to.

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
lucas_ said:
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?

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
Jazzdude said:
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.

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
Again, what is your Hamiltonian? If you ask for eigenvalues and eigenstates of the Hamiltonian, you have to specify it.
 
  • #7
Jazzdude said:
Again, what is your Hamiltonian? If you ask for eigenvalues and eigenstates of the Hamiltonian, you have to specify it.

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
The position operator only acts on a single particle state space. Its eigenstates are therefore the same as in the single particle case.
 
  • #9
Jazzdude said:
The position operator only acts on a single particle state space. Its eigenstates are therefore the same as in the single particle case.

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

1. What are eigenvalues of entanglement?

Eigenvalues of entanglement are a mathematical concept used to describe the amount of entanglement between two quantum systems. They represent the possible outcomes of a measurement on the entangled systems, and can range from 0 (no entanglement) to 1 (perfect entanglement).

2. How are eigenvalues of entanglement calculated?

Eigenvalues of entanglement are calculated using the Schmidt decomposition, which involves finding the eigenvalues and eigenvectors of the reduced density matrix of the entangled systems. This allows for a quantification of the entanglement between the systems.

3. What is the significance of eigenvalues of entanglement?

Eigenvalues of entanglement are important because they provide a measure of the entanglement between quantum systems, which is a crucial resource for many applications in quantum information processing. They also have connections to other areas of physics, such as quantum phase transitions and quantum chaos.

4. Can eigenvalues of entanglement be experimentally measured?

Yes, eigenvalues of entanglement can be experimentally measured using various techniques such as quantum state tomography or entanglement witness measurements. These methods allow for the determination of the entanglement between systems and the corresponding eigenvalues.

5. How do eigenvalues of entanglement relate to quantum entanglement?

Eigenvalues of entanglement are directly related to quantum entanglement, as they provide a quantitative measure of the entanglement between systems. The larger the eigenvalue, the more entangled the systems are, and vice versa. They are also used to quantify the entanglement in various types of entangled states, such as Bell states and GHZ states.

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