Some thoughts about no-cloning, fan-out and Quantum teleportation
The non-cloning theorem says it’s not possible to copy the state of one qubit to another.
Say, in a state psi = a |0> + b | 1>, we have no way to copy the coefficients a and b to another qubit.
To know the state, it is necessary to measure, and when measuring, the wave function collapses to 0 or 1, and we lose the coefficients.
There is an important practical consequence, the fan-out is not possible. The fan-out is to take the value of one bit and copy it several times to apply the signal to other parts of a circuit.
With classic bits, it’s pretty simple to do the fan-out. Zero is no presence of current, one is the presence, and we need just a wire to conduct the electric current and a battery strong enough to support the circuit.
In the quantum case, imagine a single atom having the state of an electron controlled by lasers. Or a single photon, being polarised, reflected, manipulated. There is no way to divide the atom or the photon without radically changing its properties, there is no fan-out.
And there is also no feedback loop on quantum circuits, for the same practical reason.
Behind the non-cloning theorem, there is the principle of Heisenberg’s uncertainty: it is not possible to determine the position and momentum of a quantum particle simultaneously.
The name “uncertainty” is not good, a better word would be “indetermination”. Because uncertainty gives the impression we don’t know, but there may be a way to determine both position and moment. Indeterminacy is another idea, that it is really impossible, by nature, to have both and this is exactly what the theory predicts.
Physicist Richard Feynman said the principle of uncertainty protects quantum mechanics. All the strange properties of quantum physics would be undone if the principle of uncertainty were not true.
For example, if it was possible to clone the state of a photon, the uncertainty principle would be destroyed. A clone would suffice. In the original, I determine the position accurately. In the clone, I determine the moment accurately. And therefore we would have both…
Okay, so it’s not possible to clone. But it is possible to teleport! It’s not like Star Trek, that the guy enters a capsule, is destroyed and reconstituted. Actually, the idea here is much more modest. The state |psi>= a |0> + b |1> is measured, and it is destroyed, the result is sent by a traditional channel to a previously entangled qubit, and this qubit can be manipulated to get the state |psi> back.
Therefore, the ideas here are entangled, and they are consistent with each other: non-cloning, uncertainty, teleport, not fan-out and others.