Simple construction of quantum universal variable-length source coding

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(\overline{\rho}_p), tend to 0. If H(\overline{\rho}_p) is estimated, we can compress the coding rate to the admissible rate H(\overline{\rho}_p) with a probability close to 1. However, when we perform a naive measurement for the estimation of H(\overline{\rho}_p), the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of H(\overline{\rho}_p) 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.