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Simple construction of quantum universal variable-length source coding

Masahito Hayashi·Keiji Matsumoto
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Abstract

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

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Masahito Hayashi, Keiji Matsumoto. 2002-11-28. Simple construction of quantum universal variable-length source coding. https://arxiv.org/abs/quant-ph/0209124

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