For pure tripartite states, the optimal deterministic rate is the minimum of two min-entropies of entanglement, and the direct and strong converse error exponents are given by explicit rate formulas.
Exponents of quantum fixed-length pure state source coding
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abstract
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. (PRL, 81, 1714 (1998))'s universal code. In the direct part, a group representation theoretical type method is essential. In the converse part, Nielsen and Kempe (PRL, 86, 5184 (2001))'s lemma is essential.
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Error exponents for tripartite-to-bipartite entanglement transformations
For pure tripartite states, the optimal deterministic rate is the minimum of two min-entropies of entanglement, and the direct and strong converse error exponents are given by explicit rate formulas.