The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Classification of multipartite entangled states by multidimensional determinants
Open accessAbstract
We find that multidimensional determinants ``hyperdeterminants,'' related to entanglement measures (the so-called concurrence, or 3-tangle for two or three qubits, respectively), are derived from a duality between entangled states and separable states. By means of the hyperdeterminant and its singularities, the single copy of multipartite pure entangled states is classified into an onion structure of every closed subset, similar to that by the local rank in the bipartite case. This reveals how inequivalent multipartite entangled classes are partially ordered under local actions. In particular, the generic entangled class of the maximal dimension, distinguished as the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the $n>~4$ qubits), contrary to the widely known bipartite or three-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical n-partite entangled states. Our classification is also useful for the mixed states.
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Cites
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Cited by
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
Scott, A. J. (2004) · Physical Review A · doi:10.1103/physreva.69.052330 · Cited by 353
Byrd, M. S., & Khaneja, N. (2003) · Physical Review A · doi:10.1103/physreva.68.062322 · Cited by 268
Fundamentals of universality in one-way quantum computation
Nest, M. V. D., Dür, W., Miyake, A., & Briegel, H. J. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/6/204 · Cited by 97
Self-citation
Metadata
- Authors
- Miyake, A.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2003-01-30
- Volume
- 67
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2005813528
- Cited by
- 273
- References
- 28
- FWCI
- 18.73
- Type
- journal article
- Language
- en
- Open access
- green
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