Entanglement criterion for identical particle

[AliceBob]

Hi, it's my first time to post here.

I'm wondering how we can define "entanglement" for identical particles.

More simply, when two bosons are in the following state
( |psi (x) >|phi (y) > + |psi (y) >|phi (x) > ) ,
are they entangled or not?I have (at least) two ideas:

1. We can define "entanglement of identical particles" only if the wave packet of each particle does not overlap (so that the two particles are distinguishable).

2. We always use the second quantization:
particles are NOT entangled if and only if the state can be written as the product of creation operators times vacuum.
(in the LaTeX style,) a_{k_1}^\dagger a_{k_2}^\dagger \cdots a_{k_N}^\dagger |vac>The second idea comes from the following paper: http://prola.aps.org/abstract/PRA/v67/i2/e024301

 

[QuantumBend]

Hi, it's my first time to post here.

I'm wondering how we can define "entanglement" for identical particles.

More simply, when two bosons are in the following state
( |psi (x) >|phi (y) > + |psi (y) >|phi (x) > ) ,
are they entangled or not?


I have (at least) two ideas:

1. We can define "entanglement of identical particles" only if the wave packet of each particle does not overlap (so that the two particles are distinguishable).

2. We always use the second quantization:
particles are NOT entangled if and only if the state can be written as the product of creation operators times vacuum.
(in the LaTeX style,) a_{k_1}^\dagger a_{k_2}^\dagger \cdots a_{k_N}^\dagger |vac>


The second idea comes from the following paper: http://prola.aps.org/abstract/PRA/v67/i2/e024301

Coherent laser photon not overlap - so what mean then? Only I must pay money for reading papers - no good, Why this?

 

[Entropia]

Hi there,

Thank you for your post. The concept of entanglement for identical particles is a complex and ongoing topic of research in quantum mechanics. The example you provided with two bosons in a superposition of position states is a commonly used scenario to explore this concept.

To answer your question, it is important to first understand the definition of entanglement. Entanglement occurs when two or more particles are in a quantum state that cannot be described independently of each other. This means that the state of one particle is dependent on the state of the other, even if they are physically separated.

In the case of identical particles, it is true that we cannot distinguish between them based on their individual properties. However, the concept of entanglement still applies. This is because even though the particles may have identical properties, their quantum states can still be correlated and dependent on each other.

The first idea you suggested, where the particles must be distinguishable for entanglement to occur, is not entirely accurate. In quantum mechanics, particles can be entangled even if they are indistinguishable.

The second idea, using second quantization to determine entanglement, is a valid approach. It is often used in theoretical studies to analyze entanglement in systems with identical particles. However, this approach may not always be applicable to real-world systems.

In summary, the concept of entanglement for identical particles is still an active area of research and there is no one definitive answer. Both of your ideas have merit and are used in different contexts. It is important to consider the specific system and context when determining if identical particles are entangled or not.

I hope this helps to clarify the concept of entanglement for identical particles. Thank you for your post and welcome to the community!