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?