The quantum Schur and Clebsch-Gordan transforms: I. efficient qudit circuits
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate H(ρp), tend to 0. If H(ρp) is estimated, we can compress the coding rate to the admissible rate H(ρp) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(ρp), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(ρp) and the non-demolition of the input state. Our protocol can be used not only for the Schumacher's scheme but also for the compression of entangled states.