Monday, September 26, 2016

No-Cloning is not fundamental

Complexity theorist Scott Aaronson makes a big deal out of the No-cloning theorem:
The subject of this talk is a deep theorem that stands as one of the crowning achievements of our field. I refer, of course, to the No-Cloning Theorem. Almost everything we’re talking about at this conference, from QKD onwards, is based in some way on quantum states being unclonable. ...

OK, but No-Cloning feels really fundamental. One of my early memories is when I was 5 years old or so, and utterly transfixed by my dad’s home fax machine, ...

The No-Cloning Theorem represents nothing less than a partial return to the view of the world that I had before I was five. It says that quantum information doesn’t want to be free: it wants to be private. There is, it turns out, a kind of information that’s tied to a particular place, or set of places. It can be moved around, or even teleported, but it can’t be copied the way a fax machine copies bits.

So I think it’s worth at least entertaining the possibility that we don’t have No-Cloning because of quantum mechanics; we have quantum mechanics because of No-Cloning — or because quantum mechanics is the simplest, most elegant theory that has unclonability as a core principle.
No-Cloning sounds fundamental, but it is not.

The theorem says that there is no physical process that always perfectly duplicates a given physical entity. You can have a laser beam that emits identical photons in identical states, but you can not have some trick optical device that takes in any photon and copies it into an additional photon in the same state.

The proof assumes that any such process would have to perfectly represent the entity (eg photon) by a wave function, to apply a unitary transformation to duplicate it, and to perfectly realize that result.

So you have to believe that a physical entity is exactly the same as a mathematical wave function, and a physical process is exactly the same as a unitary transformation.

But isn't that the essence of quantum mechanics? No, it is not.

Quantum mechanics is a system of using wave functions to predict observables. But there is no good reason to believe that there is a one-to-one correspondence between physical entities and wave functions.

The no-cloning theorem is a big headache for quantum computing because it means that qubits can never be copied. Ordinary computers spend most of their time copying bits.

But scalable qubits may not even be possible.

The no-cloning theorem is not something with any direct empirical evidence. It is true that we have no known way of duplicating an atomic state, but that is a little misleading. We have no way of doing any observations at all on an atomic state without altering that state.

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