Scheme of coding and decoding in high-dimensional quantum system

Scheme of quantum coding and decoding in the case of high-dimensional quantum states is investigated. Based on the research on coding in pure state of bi-qubits, pure state of bi-qudit, pure state of multi-qubits, and pure state of multi-qudits are studied in detail, the measurement basis of these cases are constructed respectively and the forms of unitary operators corresponding to the basis are chosen. Under these operators the largest probability by tuning up the coefficients of the measurement can be gained. Utilizing the relation between mixture states and entangled pure states, this coding and decoding in high-dimensional quantum states scheme is also generalized into mixed state case.