# Does the teleportation protocol work for any dimension? [duplicate]

Suppose Alice and Bob share a maximally entangled state in $$d$$ dimensions i.e

$$\vert\phi\rangle = \frac{1}{\sqrt{d}}\sum_{i=1}^d \vert i\rangle\vert i\rangle$$

Given a state $$d$$ dimensional $$\rho$$, the standard teleportation protocol is for $$d=2$$. This does a Bell measurement on the qubit and one half of the maximally entangled state, the measurement result is sent to Bob and Bob applies one of four possible unitaries.

Does the same procedure generalize for all $$d$$? If so, what is Alice's measurement and what are the unitaries that Bob applies?