2013
DOI: 10.1103/physreva.88.032323
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Compatible quantum correlations: Extension problems for Werner and isotropic states

Abstract: 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 … Show more

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Cited by 23 publications
(39 citation statements)
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“…It is clear that is maximized for and . Therefore, This result can be readily used to characterize the extendibility of isotropic states, providing an alternative proof of the result by Johnson and Viola [ 53 ].…”
Section: Port-based Teleportationsupporting
confidence: 57%
“…It is clear that is maximized for and . Therefore, This result can be readily used to characterize the extendibility of isotropic states, providing an alternative proof of the result by Johnson and Viola [ 53 ].…”
Section: Port-based Teleportationsupporting
confidence: 57%
“…We note that our bound, though not optimal, is a close approximation of the necessary and sufficient condition ψ − ≥ −(d − 1)/k proved in [40] for the k-symmetric extendability of Werner states. This also proves that the k-symmetric extension and k-bosonic extension problems are generally different.…”
Section: For Detailsmentioning
confidence: 72%
“…Unfortunately, for any higher dimensions a full characterization involving only spectra is highly unlikely [22]. There have been some efforts made for special cases but no general results found [41][42][43]. Nevertheless, our physical picture based on the convexity of B and the symmetry of the system may shed light on the understanding of symmetric extendibility for higher dimensional systems.…”
Section: Theoremmentioning
confidence: 99%