Exponents of quantum fixed-length pure-state source coding

We derive the optimal exponent of the error probability of the quantum fixed-length pure-state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al.’s [Phys. Rev. Lett. 81, 1714 (1998)] universal code. In the direct part, a group representation theoretical type method is essential. In the converse part, Nielsen and Kempe’s [Phys. Rev. Lett. 86, 5184 (2001)] lemma is essential.