No-Cloning-Theorem
The no -cloning theorem is an important result of quantum physics. Accordingly, it is not possible to build a system which perfectly copied any qubit to another qubit, without altering the original. The reason for this lies in the linearity of quantum mechanics.
The no -cloning theorem has far-reaching consequences for the quantum computer science. On the one hand conventional error correction codes based on the copy information to be transmitted can not be used. Secondly, no one can listen to a corresponding transmission of information unnoticed, since he would have to make a copy of the transmitted qubits. This property forms the basis of quantum cryptography.
Trigger the discovery of the no- cloning theorem was a work of Nick Herbert, in which he showed how a superluminal information transfer would be possible by copying qubits. William Wootters and Wojciech Zurek published in 1982, the no- cloning theorem and have thus shown that there can be no superluminal information transmission in this way.
Evidence
For the proof of the no -cloning theorem, it is assumed that a quantum mechanical methods exist, copy the arbitrary qubits perfectly. This assumption is subsequently leads to a contradiction.
There were, and any two states that are to be copied to one of them independent state. Since scalar products ( and probabilities ) are to be obtained, the procedure required for this can only be described by a unitary map. This must have to copy form the following properties:
For the scalar product thus can specify the following two equations:
The first equation follows this by inserting the above equations, while results in the second equation, since unitary images do not change the scalar product. Thus we obtain
As well as due to the compatibility of scalar and tensor
So there follows
This equation has only solutions. This means that either (if ) are orthogonal and or (if ). Thus, a quantum mechanical process that is able to duplicate a state at best, to copy all of the orthogonal states. However, copying is not possible any conditions.
Swell
- Quantum computer science