In quantum mechanics, the no-cloning theorem states
there is no general way to make copies of an arbitrary quantum state .
This has profound implications for quantum information.
To prove this theorem, let us pretend that a machine exists
that can do just that: copy arbitrary quantum states.
Given an input and a blank ,
this machines turns into :
We can use this device to make copies of the basis vectors and :
If we feed this machine a superposition ,
we want the following behaviour:
Note the appearance of the cross terms with a factor of .
The problem is that the fundamental linearity of quantum mechanics
dictates different behaviour:
This is clearly not the same as before: we have a contradiction,
which implies that such a general cloning machine cannot ever exist.
- N. Brunner,
Quantum information theory: lecture notes,
- J.B. Brask,
Quantum information: lecture notes,