Quantum State Merging for Arbitrarily Small-Dimensional Systems

Abstract

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.

23 pages, 2 figures

References in corpus (11)

• Quantum Computing in the NISQ era and beyond
• Quantum information can be negative
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• The mother of all protocols: Restructuring quantum information's family tree
• Quantum Internet: from Communication to Distributed Computing!
• Quantum state redistribution based on a generalized decoupling
• On the distributed compression of quantum information
• Conditional Decoupling of Quantum Information
• Deterministic transformations of bipartite pure states
• Distributed Encoding and Decoding of Quantum Information over Networks
• Remote extraction and destruction of spread qubit information

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