Simple construction of quantum universal variable-length source coding

This paper describes the construction of 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(ρ~_p), tend to 0. If H(ρ~_p) is estimated, and compress the coding rate to the admissible rate H(ρ~_p) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(ρ~_p), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(ρ~_p) and the nondemolition of the input state. Our protocol can be used not only for the Schumacher´s compression but also for the compression of entangled states.