Alphabets from the information source (ρ1, ρ2, ρ3, ...) are first converted into bit sequences by the source encoder so as to compress original messages into smaller bits. Essentially, source coding entails representation of common alphabet in a message as short sequences of bits, and uncommon alphabet as longer sequences, to make the average length of the coded message as short as possible. The unequal frequencies of the letters imply a redundancy that enables the compression of the message. The outputs from the source encoder are further encoded by the channel encoder into appropriate code words by adding some redundant bits to protect information from noise disturbances in the channel. An output from the channel is generally different from an input code word due to noise. Then at the receiving side, we try to decode the original signal by applying appropriate error correction. Finally we decompress the decoded signal to restore the original messages.

Shannon established information theory by quantifying the effectiveness and the limits of these codings in 1948. Shannon's information theory is a quite mathematical and hence very general theory. Unfortunately, however, Shannon's information theory is not perfect modeling of physics behind information. Information theory should eventually be represented by the words of quantum mechanics. It is quite recently, after 90's, when such representations are clarified.

In quantum information theory, alphabets in the above viewgraph ρ1, ρ2, ρ3, ... are now the density matrices representing quantum states of signals. When one considers coding with these quantum states explicitly, one can entails quantum effects to overcome the performances in conventional theory. For example;

(1) In compression process, when the quantum states are non-commuting with each other, then there is another redundancy that does not have any classical counterpart, and further compression is possible even if these quantum alphabets appear with equal frequencies. (Quantum source coding)

(2) Concerning channel coding, one may consider a decoding process assisted by a quantum computation, i.e. a decoding by entangling the letter quantum states prior to the final measurement. One can then attain a higher capacity than the Shannon capacity limit. (Quantum channel coding)

We have been working on how to demonstrate these predicted quantum effect experimentally. Although it is still a formidable task to implement quantum coding by using quantum gates working on practical quantum particles for communications, it is possible to test the basic concepts of quantum information theory with currently available photonic technologies.