Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2

Abstract

Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.

27 pages, 1 figure; added new references and improved the presentation

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Cited by in corpus (27)

• Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
• The maximally entangled set of multipartite quantum states
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Transformations among Pure Multipartite Entangled States via Local Operations Are Almost Never Possible
• Operational multipartite entanglement measures
• Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication
• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• Transformations of $W$-Type Entangled States
• Multi-copy and stochastic transformation of multipartite pure states
• The maximally entangled set of 4-qubit states
• Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes
• The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC
• Complete set of operational measures for the characterization of 3-qubit entanglement
• Multipartite correlations in mutually unbiased bases
• Deterministic LOCC transformation of three-qubit pure states and entanglement transfer
• The source and accessible entanglement of few-body systems
• Measurement outcomes that do not occur and their role in entanglement transformations
• Local Transformations of Multiple Multipartite States
• State transformations within entanglement classes containing permutation-symmetric states
• On the Geometric Measures of Entanglement
• Deterministic transformations of bipartite pure states
• Deterministic transformations of three-qubit entangled pure states
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
• 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
• Approximate and ensemble local entanglement transformations for multipartite states
• Multipartite entanglement theory with entanglement-nonincreasing operations