The Research Of Entanglement-assisted Quantum Convolutional Coding

Quantum convolutional coding is to assure the integrity of information in the transmissionin quantum communication. Therefore, the study on the theoretical research and the realizationof the quantum coding is very important.In general there are two ways to encode a quantum state, one is the use of block code,another is to use convolutional code. Implementations of two coding have a great relation tostabilizer, and the research on quantum coding in this thesis is also based on stabilizer.We investigate several classes of quantum convolutional coding. Entanglement-assistedquantum convolutional coding using finite-depth operation and infinite-depth operation arestudied. The encoding circuit and decoding circuit of them are also given. In entanglement-assisted quantum convolutional coding using infinite-depth operation, the sender in quantumcommunication need to perform an infinite-depth operation for encoding, but the receiver candecode by performing finite-depth operations only. We also discuss quantum convolutionalcoding without entanglement-assisted. The details are as follows: Suppose that H₁(D) andH₂(D) are the respective check matrices corresponding to noncatastrophic, delay-free encodersfor classical binary convolutional code C₁ and C₂. If the invariant-factors of H₁(D)H₂^T (D^-1)are of the form D^l (l is a integer), then both the encoding and decoding can be realized by usingfinite depth operations in the resulting entanglement-assisted quantum convolutional code. Ifthe invariant-factors of H₁(D)H₂T (D^-1) are not all of the form Dl, then an infinite-depth oper-ation is needed in encoding to construct entanglement-assisted quantum convolutional code. IfH₁(D)H₂^T (D^-1) = 0, then we can construct quantum convolution code without entanglement-assisted.