The Entanglement of Formation for Isotropic States

Barbara M. Terhal; Karl Gerd H. Vollbrecht

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The Entanglement of Formation for Isotropic States

Barbara M. Terhal, Karl Gerd H. Vollbrecht

Quantum Physics · Submitted 16 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,982 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.64 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.72 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.53	0.95	0.74	asserted 1.00
s1	For two qutrit isotropic states we determine the convex hull and we have strong evidence for its exact form for arbitrary dimension.	result 0.50	0.94	0.18	asserted 0.61
s2	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.	result 0.98	0.93	0.40	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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arXiv listing abstract v1

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figures and tables
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P abstract

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S sections
T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

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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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A resource theory of asynchronous quantum information processing
quant-ph 2025-04 unverdicted novelty 7.0 of 10

Introduces resource theories for asynchronous port-based teleportation with free classical and quantum pre-processing, computes tight fidelity bounds for isotropic, graph, and symmetrized EPR states, and proves the st...
Certification of high-dimensional entanglement in continuous-variable systems
quant-ph 2026-10 accept novelty 5.0 of 10

A new fidelity-based Schmidt-number witness for two-mode continuous-variable states is evaluated from the covariance matrix alone and certifies entanglement dimension for Gaussian and non-Gaussian states.

How the literature uses it

2 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Builds on it 1 paper

In this work, we expand on existing methods [ref] to compute the convex roofs of many more entanglement monotones for these classes of symmetric states and more.

Entanglement monotones and transformations of symmetric bipartite states · Introduction · 0.94

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