2013/05/31 by Peter D. Johnson, Lorenza Viola
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.88.032323
published as Phys. Rev. A 88, 032323 (2013) · 19 pages, 6 figures, 1 Table. Added results address isotropic states. Proofs moved to appendices. Minor clarifications added and Eq. (B1) fixed
arxiv created 2013/09/11 · openalex publication_date 2013/09/27 · arxiv updated 2013/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state ``joins'' the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N-representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.