In $|x_1,...,x_n\rangle$, can the individual constituents be called qubits?

Question

A qubit is a quantum system in which the Boolean states 0 and 1 are rep- resented by a prescribed pair of normalised and mutually orthogonal quantum states labeled as ${|0⟩, |1⟩}$

According to [1]. Then a quantum register $\mid x_1x_2...x_n\rangle, x_i\in\{0,1\}$ is defined to be collection of n qubits.

Now I often see expressions like $\mid x_1, ... x_n \rangle$ where the $x_i$ belong to some $S \subset \mathbf{Z}$.

1. Can the individual constituents $\mid x_i \rangle$ be called qubits even though they are non-binary?
2. Would it be appropriate to call $\mid x_1, ... x_n \rangle$ a qubit register in this case?
3. What is the physical interpretation of such a register?

Answer 1

The $|x_i\rangle$ you mention here are qudits, they are the generalization of qubits to base $d$ with $|S| = d$. It is categorized by a superposition of $d$ states, same way a qubit is described by the superposition of 2 states.
In base 3 it has a specific name as well, this is called qutrit.