Entanglement criterion for identical particle

• AliceBob
In summary, the conversation discusses the concept of entanglement for identical particles, specifically when two bosons are in a certain state. The conversation presents two ideas for defining entanglement for identical particles: one based on distinguishability and the other based on second quantization. The second idea is supported by a paper which can only be accessed by paying for it.
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

AliceBob said:
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?

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!

1. What is the entanglement criterion for identical particles?

The entanglement criterion for identical particles is a principle in quantum mechanics that states that two or more particles with identical properties (such as spin or charge) cannot be distinguished from each other. This means that their states cannot be described independently, and they are said to be entangled.

2. How does entanglement of identical particles occur?

Entanglement of identical particles can occur through various interactions, such as collisions or interactions with a common environment. The particles become entangled when their states become correlated and cannot be described independently.

3. What is the significance of entanglement of identical particles?

The entanglement of identical particles is significant because it demonstrates the non-local nature of quantum mechanics. This means that the state of one particle can affect the state of another particle, even if they are separated by large distances, and this effect is instantaneous.

4. How is the entanglement of identical particles measured?

The entanglement of identical particles can be measured using quantum entanglement criteria, such as the Bell inequality. This involves performing experiments on the entangled particles and comparing the results to theoretical predictions.

5. What are the potential applications of entanglement of identical particles?

The entanglement of identical particles has potential applications in quantum computing, quantum communication, and quantum cryptography. It also has implications for fundamental physics, as it allows for the testing of theories such as quantum entanglement and non-locality.

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