  Recent advances in quantum technology facilitate the realization of
information processing using quantum computers at least on the small and
intermediate scales of up to several dozens of qubits. We investigate
entanglement cost required for one-shot quantum state merging, aiming at
quantum state transformation on these scales. In contrast to existing coding
algorithms achieving nearly optimal approximate quantum state merging on a
large scale, we construct algorithms for exact quantum state merging so that
the algorithms are applicable to any given state of an arbitrarily
small-dimensional system. In the algorithms, entanglement cost can be reduced
depending on a structure of the given state derived from the Koashi-Imoto
decomposition. We also provide improved converse bounds for exact quantum state
merging achievable for qubits but not necessarily achievable in general. As for
approximate quantum state merging, we obtain algorithms and improved converse
bounds by applying smoothing to those for exact state merging. Our results are
applicable to distributed quantum information processing and multipartite
entanglement transformation on small and intermediate scales.
