What is the relation between a Fock state and a qudit?

Question

What is the relation between a Fock state and a qudit? Is the Fock state $|n\rangle, n=0, 1, 2, ...$ a qudit having $d=\infty$?

Answer 1

I would say it is not exactly the same.

A qudit of size $d$ has a finite number of states. A Fock state can have discretely infinite number of states in principle.

The goal of having multiple qudits, let's say $N$, is to make a larger space of size $d^N$. Rarely you consider product of Fock spaces (but it can be done). Usually, you define a Fock space that includes all configurations.

Fock spaces can be fermionic or bosonic (the ladder operators have defined commutation relations). The qudits are usually neither fermions nor bosons (check how weird is the commutation algebra of qutrits).

If you have a chain of qudits, there are mappings to converting them to Fock states and viceversa. But without a mapping I would not force them to be equivalent.

You can also have continuous Fock spaces, but it would be weird to have continuous qudits?

Any way if you want to think about $d=\infty$ qudits, consider that you can always write a Fock space to describe not only your $\infty$-qdit but also a chain of $\infty$ number of $\infty$-qdit. The Fock space is just more general.