Quantum Information Theory
The theory of quantum information is a result of the effort to generalize classical information theory to the quantum world. Quantum information theory aims to investigate the following question:
What happens if information is stored in a state of a quantum system?
One of the strengths of classical information theory is that physical representation of information can be disregarded: There is no need for an 'ink-on-paper' information theory or a 'DVD information' theory. This is because it is always possible to efficiently transform information from one representation to another. However, this is not the case for quantum information: it is not possible, for example, to write down on paper the previously unknown information contained in the polarisation of a photon.
In general, quantum mechanics does not allow us to read out the state of a quantum system with arbitrary precision. The existence of Bell correlations between quantum systems cannot be converted into classical information. It is only possible to transform quantum information between quantum systems of sufficient information capacity. The information content of a message can, for this reason, be measured in terms of the minimum number n of two-level systems which are needed to store the message: consists of n qubits. In its original theoretical sense, the term qubit is thus a measure for the amount of information. A two-level quantum system can carry at most one qubit, in the same sense a classical binary digit can carry at most one classical bit.
As a consequence of the noisy-channel coding theorem, noise limits the information content of an analog information carrier to be finite. It is very difficult to protect the remaining finite information content of analog information carriers against noise. The example of classical analog information shows that quantum information processing schemes must necessarily be tolerant against noise, otherwise there would not be a chance for them to be useful. It was a big breakthrough for the theory of quantum information, when quantum error correction codes and fault-tolerant quantum computation schemes were discovered.
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