In most models of quantum computing, the inputs are classical bits and the outputs are probabilistic classical bits. They can be freely duplicated etc. The proof goes through as normal, with the usual caveats that apply when dealing with probabilistic processes. For example, you have to replace the conclusion with “you cannot devise a quantum algorithm such that for any e>0 supplied to the algorithm, it gives the incorrect answer with probability at most e”.
You can employ a model of quantum computing in which both the inputs and outputs are qbits. Such models are used for internal operations of quantum computers, but they aren’t much use for modelling the interface with the decoherent outside world, and you still end up with a corresponding version of the theorem holding anyway.
In most models of quantum computing, the inputs are classical bits and the outputs are probabilistic classical bits. They can be freely duplicated etc. The proof goes through as normal, with the usual caveats that apply when dealing with probabilistic processes. For example, you have to replace the conclusion with “you cannot devise a quantum algorithm such that for any e>0 supplied to the algorithm, it gives the incorrect answer with probability at most e”.
You can employ a model of quantum computing in which both the inputs and outputs are qbits. Such models are used for internal operations of quantum computers, but they aren’t much use for modelling the interface with the decoherent outside world, and you still end up with a corresponding version of the theorem holding anyway.