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Quantum information theory: example problems

1 Classical information through quantum channels

classical information theory has two basic theorem: Shannon’s noiseless channel coding theorem and Shannon’s noisy channel coding theorem. First one gives number of how many qubits are used to store information and second tells how reliable these information are which can help to correct the noise.

Shannon entropy is used to evaluate the classical source distribution. the next step is to investigate the problem of transmitting classical information through a noisy quantum channel. Quantum mechanics gives us a huge variety of noise models, since it takes place in a continuous space, and it is not at all obvious how to adapt classical error-correction techniques to combat the noise.

2 Quantum information through quantum channels

Schumacher’s noiseless channel coding theorem quantifies the resources required to do quantum data compression, with the restriction that it be possible to recover the source with fidelity close to 1

3 Quantum distinguishability

it is possible to distinguish between the two possibilities with perfect certainty. quantum mechanically it is not always possible to distinguish between arbitrary states.