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Exponentially many entanglement and correlation constraints for multipartite quantum states

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Christopher Eltschka, Felix Huber, Otfried Gühne, Jens Siewert

Quantum Physics · Submitted 24 Jul 2018

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

The authors' main claim We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension.

how it is stated · asserted 1.00 read the record →

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arXiv ID1807.09165 (version 1)
Pith IDNQDHOR5X, Pith's permanent record of this paper and its review
CitationChristopher Eltschka, Felix Huber, Jens Siewert, Otfried G\"uhne. "Exponentially many entanglement and correlation constraints for multipartite quantum states." arXiv:1807.09165 (2018). https://pith.science/paper/NQDHOR5X
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The compiled record

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, 4,837 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.63 · compares with prior results 0.54 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating the generalized state inversion map. This map provides a systematic way to generate local unitary invariants of degree two in the state and is directly linked to the shadow inequalities proved by Rains [IEEE Trans. Inf. Theory 46, 54 (2000)]. The constraints are stated in terms of linear inequalities for the linear entropies of the subsystems. For pure quantum states they turn into monogamy relations that constrain the distribution of bipartite entanglement among the subsystems of the global state.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. contribution 0.97 0.92 0.49 asserted 1.00
s1 The size of this family is exponential in the number of subsystems. result 0.81 0.80 0.22 asserted 1.00
s2 We obtain these relations by defining and investigating the generalized state inversion map. method 0.94 0.94 0.07 asserted 1.00
s3 This map provides a systematic way to generate local unitary invariants of degree two in the state and is directly linked to the shadow inequalities proved by Rains [IEEE Trans. Inf. Theory 46, 54 (2000)]. method 0.83 0.65 0.07 asserted 1.00
s4 The constraints are stated in terms of linear inequalities for the linear entropies of the subsystems. result 0.69 0.82 0.19 asserted 1.00
s5 For pure quantum states they turn into monogamy relations that constrain the distribution of bipartite entanglement among the subsystems of the global state. interpretation 0.73 0.82 0.29 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • full text
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  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • 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 present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating the generalized state inversion map. This map provides a systematic way to generate local unitary invariants of degree two in the state and is directly linked to the shadow inequalities proved by Rains [IEEE Trans. Inf. Theory 46, 54 (2000)]. The constraints are stated in terms of linear inequalities for the linear entropies of the subsystems. For pure quantum states they turn into monogamy relations that constrain the distribution of bipartite entanglement among the subsystems of the global state.

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References
How the literature uses it

4 arXiv papers cite this in 4 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 · 2 sentences without a confident label

Cites it as background 2 papers

What it cites · 6 sentences without a confident label

Cites as background 1 paper

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