Entanglement and two particle system

In summary, during the conversation, the speaker talks about the concept of entanglement and its relation to the total angular momentum of a two-particle system. They also mention the possibility of measuring properties of one particle in a two-particle state and how it affects the overall state. The speaker also provides a resource for further understanding of the topic.
  • #1
J.Asher
12
0
Hello, I am planning to talk about the entanglement for the presentation but now I am a bit confused of between entanglement and many-particle system. Actually, I have only studied two-particle system when dealing the total angular momentum. let me assume that there are a photon and an electron then the total angular momentum might be 3/2. So the possible states describing the system would be |3/2, 3/2>, |3/2,1/2>, |3/2, -1/2>, |3/2, -3/2>, |1/2, 1/2>, |1/2, -1/2>. Here, for example if I write down |3/2, 1/2> in terms of the production states of particle 1 and 2, I can say c_1|1,1>|1/2,-1/2> + c_2|1,0>|1/2,1/2> (c_1 and c_2 are normalized constants). If I write down again nicely :D
|3/2,1/2> = c_1|1,1>|1/2,-1/2> + c_2|1,0>|1/2,1/2>.
But it look totally the same as the wave function of the entangled system.
So can I say that If I measure 1h/2pi by operating z component momentum upon photon, then it is obviously the electron lies on the state |1/2, -1/2> ... ?
Or is it impossible to operate the momentum operator of particle 1 or 2 upon this |3/2,1/2>.
(Actually, I am also confused of meaning of |3/2,1/2>, what exactly does is says...?)

Thx for reading.
 
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  • #2
If the Hamiltonian describing your system has rotational invariance, then every state of a particular energy (energy eigenstate), will also have a particular value for those two angular-momentum numbers, which in your case is 3/2 and 1/2.

For a given z-axis in space, |3/2,1/2> means a state with total angular momentum 3/2 and with angular momentum 1/2 about the z-axis (in units of hbar). I.e. the projection of the angular momentum vector along the z-axis is 1/2.

In your case, |3/2,1/2> denotes a two-particle state. It is then possible to write that state as a linear combination of products of single-particle states, as you have done in your post.

When a two-particle state cannot be written as one product of one-particle states, it is said to be entangled. So if both your coefficients c1 and c2 are non-zero, the two-particle state is entangled.

For a two-particle state, it is always (in theory) possible to measure properties of one of them. When this is done you will obtain a quantum number for that particle, and at the same time the full two-particle state will collapse in the usual way, and you then know without measuring some thing about the other particle.

In your example, that would mean that if you measure the z-component of spin on one particle to be 1, then the z-component of angular momentum for the other particle must be -1/2 as you say.

That was my understanding, but don't take it as gospel...

These lecture notes are pretty good:
http://www.uio.no/studier/emner/matnat/fys/FYS4110/h10/undervisningsmateriale/LectureNotes2010.pdf" [Broken]
 
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  • #3
When a two-particle state cannot be written as one product of one-particle states, it is said to be entangled. So if both your coefficients c1 and c2 are non-zero, the two-particle state is entangled.
What does it mean? I think if c1 and c2 are non-zero, it does means that the two-particle state can be described in a product of two single-particle states...?
 

1. What is entanglement in a two particle system?

Entanglement is a phenomenon in quantum mechanics where two particles become connected in such a way that the state of one particle cannot be fully described without considering the state of the other particle, even if they are separated by a large distance.

2. How does entanglement occur in a two particle system?

Entanglement can occur through the process of quantum superposition, where particles can exist in multiple states simultaneously. When two particles interact, they can become entangled and share a combined state that cannot be described independently.

3. What are the implications of entanglement in a two particle system?

Entanglement has many implications in quantum mechanics, including the potential for instantaneous communication over long distances, quantum teleportation, and the ability to perform calculations and measurements more accurately than with classical systems.

4. How is entanglement measured in a two particle system?

Entanglement can be measured through various techniques, such as quantum state tomography, where the state of the particles is measured multiple times to determine their entanglement. Other methods include Bell inequality tests and entanglement witnesses.

5. Can entanglement in a two particle system be used for practical applications?

While entanglement has been demonstrated in experiments, it is still a relatively new and complex phenomenon that is not fully understood. However, researchers are exploring potential practical applications, such as quantum computing and secure communication, that could utilize entanglement in the future.

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