Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions

Abstract

We introduce and analyze graph-associated entanglement cost, a generalization of the entanglement cost of quantum states to multipartite settings. We identify a necessary and sufficient condition for any multipartite entangled state to be constructible when quantum communication between the multiple parties is restricted to a quantum network represented by a tree. The condition for exact state construction is expressed in terms of the Schmidt ranks of the state defined with respect to edges of the tree. We also study approximate state construction and provide a second-order asymptotic analysis.

19 pages, 7 figures, published version

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• Hierarchy of quantum operations in manipulating coherence and entanglement
• Entanglement cost for infinite-dimensional physical systems
• Distributed Encoding and Decoding of Quantum Information over Networks
• Transformations in quantum networks via local operations assisted by finitely many rounds of classical communication
• Identifying families of multipartite states with non-trivial local entanglement transformations
• Distillation of multipartite entangled states for arbitrary subsets of parties in noisy quantum networks of increasing size