Localizable Entanglement

F. Verstraete; J. I. Cirac; M. A. Martin-Delgado; M. Popp

RECORD

Localizable Entanglement

M. Popp, F. Verstraete, M. A. Martin-Delgado, J. I. Cirac

Quantum Physics · Submitted 17 Nov 2004

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

The authors' main claim We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel.

how it is stated · hedged possibility 0.67 read the record →

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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, 6,787 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.

background contribution method result interpretation main claim

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 consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins.	contribution 0.95	0.85	0.11	asserted 0.68
s1	This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations.	interpretation 0.56	0.53	0.10	asserted 0.96
s2	For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions.	result 0.79	0.95	0.20	asserted 1.00
s3	We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins.	method 0.89	0.93	0.08	asserted 0.74
s4	The virtues of LE are illustrated for various spin models.	contribution 0.65	0.80	0.06	asserted 0.99
s5	In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed.	result 0.76	0.78	0.13	asserted 0.79
s6	We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length.	result 0.97	0.89	0.08	asserted 0.99
s7	We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel.	result 0.96	0.94	0.15	hedged possibility 0.67
s8	Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.	contribution 0.91	0.95	0.06	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.66 · evidence from simulation or computation 0.67.

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full text
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S sections
T body sentences
C citations
R cross-paper relations

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 consider systems of interacting spins and study the entanglement that can be localized, on average, between two separated spins by performing local measurements on the remaining spins. This concept of Localizable Entanglement (LE) leads naturally to notions like entanglement length and entanglement fluctuations. For both spin-1/2 and spin-1 systems we prove that the LE of a pure quantum state can be lower bounded by connected correlation functions. We further propose a scheme, based on matrix-product states and the Monte Carlo method, to efficiently calculate the LE for quantum states of a large number of spins. The virtues of LE are illustrated for various spin models. In particular, characteristic features of a quantum phase transition such as a diverging entanglement length can be observed. We also give examples for pure quantum states exhibiting a diverging entanglement length but finite correlation length. We have numerical evidence that the ground state of the antiferromagnetic spin-1 Heisenberg chain can serve as a perfect quantum channel. Furthermore, we apply the numerical method to mixed states and study the entanglement as a function of temperature.

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References

Forward citations

Cited by 5 Pith papers

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

Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
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For uniform single-occupancy post-selection on m rungs of two identical Gaussian fermion states, the conditional residual state factorizes into m universal entangling modes and N-2m spectator modes, giving entanglemen...
Measurement-induced entanglement Hamiltonian
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In a critical free-fermion chain, after partial projective measurements the entanglement Hamiltonian is a local grand-canonical operator: a measurement-independent inverse temperature times a local chemical potential ...
Separability and entanglement of resonating valence-bond states
cond-mat.str-el 2022-12 unverdicted novelty 6.0 of 10

Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
Conformal invariance and quantum non-locality in critical hybrid circuits
quant-ph 2020-03 conditional novelty 6.0 of 10

At the measurement-driven entanglement transition in random Clifford circuits, entanglement entropy and mutual information collapse onto conformal field theory correlation functions, with real circuit time acting as i...
Entanglement and transport through correlated quantum dot
cond-mat.str-el 2006-03 conditional novelty 6.0 of 10

In a Kondo-regime quantum dot, the conductance reaches the quantum limit 2e^2/h while the pairwise charge and spin concurrence between the dot and the nearest lead atom vanish simultaneously.

How the literature uses it

8 arXiv papers cite this in 9 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 · 6 sentences without a confident label

Cites it as background 3 papers

Studies of localizable entanglement [ref] and single-round measurements [ref] have shown how local measurements can concentrate correlations or prepare nontrivial many-body states [ref] .

Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States · Introduction · 0.82
Finally, we note there exists a notion of localizable entanglement and associated entanglement length, [ref] whose divergence is connected to a string order parameter.

Spurious Long-range Entanglement and Replica Correlation Length · Discussion · 0.98
Teleportation in many-body states is often quantified by the concept of measurement-induced entanglement (MIE) [ref] and localizable entanglement [ref] .

Nonlocal growth of quantum conditional mutual information under decoherence · Comparing Different Teleportation Metrics · 0.87

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