Many good questions on this site have explored how entanglement lies at the boundary between the quantum world and the classical. For example in computational speedups, or teleportation or superdense coding, at least two qubits are entangled in some form or another, and entanglement seems to be at the heart of, or required for, the quantum improvement.
The no-cloning theorem, on the other hand, is a statement applicable to even a single qubit. Nonetheless, there is no classical analogue of the no-cloning theorem, and yet the no-cloning theorem can be the basis for interesting applications of quantum mechanics/quantum information theory.
Two "entanglement-free" applications of the no-cloning theorem that come to immediate mind are:
Although there are "entangled" versions of the above (e.g. the E91 scheme), the "entanglement-free" versions are just as valid applications of qubits.
Can qubits that are not entangled and instead in a product state be used in other interesting applications, in a manner that does not seem to have a classical analogue?
If so, are the applications merely also a version of the no-cloning theorem, or is there some other aspect of quantum information theory at play?