# Conceiving an entangling measurement on copies of a two-mode Fock state

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Consider two copies of a general pure two-mode Fock state with a definite number of photons $N$ as follows.

$|\psi\rangle^{\mathrm{TMFS}}=\sum_{n=0}^{N} c_{n}|n\rangle_{a}|N-n\rangle_{b}$ where $c_n$ are generic coefficients and $a$, $b$ are the two modes. Some specific states that fall under this class of states are the Holland-Burnett states and the N00N states (with both mode and particle entanglement).

In analogy to the Bell measurement on two qubits, how to think of a corresponding entangling measurement that could create entanglement between the two copies of $|\psi\rangle^{\mathrm{TMFS}}$. What would be the entangled two-copy basis for this measurement similar to the Bell basis?

Further, I would also like to extend it to scenarios that include more than two copies of $|\psi\rangle^{\mathrm{TMFS}}$.

Are there any good references I can go through to think of this problem in a solid way? Thanks.

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