Are Bi-photons and Fock States (with $N=2$) the same? I've been researching about quantum states of light, and I came across with both terms. For what I understand of both, I think they are the same (entangled individual photons with same position and frequency). Am I right?
Also, I'd like to ask if Fock states can be understood as an extreme squeeze of a coherent state where the uncertainty of the amplitude (or the number of photons) is zero (but this may imply an infinite uncertainty in the phase, which I don't know if makes any sense).
 A: The Fock states are states with a well-defined number of particles (photons). This number can range from zero (the vacuum state) to an arbitrary large number. However, the notion of a Fock state does not make any reference any other degrees of freedom of the photons, other than the particle-number degree of freedom. In those cases where other degrees of freedom are included, those degrees of freedom would be the same for all particles in the Fock state.
A bi-photon is any state the contains exactly two photons. Since one of the Fock states has exactly two photon, one can say that this particular Fock state is a bi-photon state. However, one usually encounter bi-photon states when the states also have particular properties associated with their other degrees of freedom.
Often bi-photon states are used to describe bi-partite entanglement. One can only have an entangled state if the state carries other degrees of freedom in addition to the particle-number degrees of freedom. For instance, the Bell-states are entangled bi-partite states
A: As per the comments, your second question is already answered and so I will only answer your first question, the title question, where you ask, Are Bi-photons and Fock States (with N=2) the same?
Biphotons are a quantum entangled state comprising of two photons.
Fock states (N=2) are quantum states that is an element of the Fock space with a well defined number of quanta.
The Fock state is an eigenstate of the number operator with an eigenvalue  n k i.
Now the difference is that a biphoton is made of two entangled particles, but there is a :


*

*single photon Fock state, and (where the entangled photons are separated, and only one is in a Fock state)

*two pieces of single photon Fock states |1⟩|1⟩, (two separately prepared photons)

*and there is one piece of two photon Fock state |2⟩. (this is what you are referring to)
The difference is that in the second case, the photons are at two different times, and in the third case, the photons are simultaneous.
So the answer is no, the two are not the same, there are different cases of a Fock state (N=2).
Please see the single photon Fock case here:
https://www.iqst.ca/quantech/research/fock.php
