Entanglement of formation for isotropic states
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We give an explicit expression for the entanglement of formation for isotropic density matrices in arbitrary dimensions in terms of the convex hull of a simple function. For two qutrit isotropic states we determine the convex hull and we have strong evidence for its exact form for arbitrary dimension. Unlike for two qubits, the entanglement of formation for two qutrits or more is found to be a nonanalytic function of the maximally entangled fraction in the regime where the density matrix is entangled.
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In arbitrary dimensions the underlying optimisation problem for entanglement of formation is unsolved apart from a few known solutions for particular states.
“In arbitrary dimensions the underlying optimisation problem is unsolved -apart from a few known solutions for particular states [59].”
From Measures and dynamics of entangled states (2005) · cites this paper as [59]
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- Authors
- Terhal, B. M., & Vollbrecht, K. G. H.
- Affiliations
- IBM Research - Thomas J. Watson Research Center (US)
- Technische Universität Braunschweig (DE)
- ORCID
- Terhal, Barbara M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2000-09-18
- Volume
- 85
- Issue
- 12
- Pages
- 2625-2628
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2043836237
- Cited by
- 254
- References
- 9
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- FWCI
- 8.27
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- entanglement of formation, isotropic states, convex hull, qutrits, non-analyticity, higher-dimensional quantum systems, entanglement measures
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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