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Bipartite matrix-valued tensor product correlations that are not finitely representable

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Samuel J. Harris

Operator Algebras · Submitted 22 Jun 2018

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

The authors' main claim We show that, for any $m,k \geq 2$ with $(m,k) \neq (2,2)$, there is an $n \leq 4$ for which we have the separation $C_q^{(n)}(m,k) \neq C_{qs}^{(n)}(m,k)$.

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arXiv ID1806.08745 (version 1)
Pith IDGEC3BTEF, Pith's permanent record of this paper and its review
CitationSamuel J. Harris. "Bipartite matrix-valued tensor product correlations that are not finitely representable." arXiv:1806.08745 (2018). https://pith.science/paper/GEC3BTEF
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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, 3,159 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.93 · compares with prior results 0.26 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We consider the matrix-valued generalizations of bipartite tensor product quantum correlations and bipartite infinite-dimensional tensor product quantum correlations, respectively. These sets are denoted by $C_q^{(n)}(m,k)$ and $C_{qs}^{(n)}(m,k)$, respectively, where $m$ is the number of inputs, $k$ is the number of outputs, and $n$ is the matrix size. We show that, for any $m,k \geq 2$ with $(m,k) \neq (2,2)$, there is an $n \leq 4$ for which we have the separation $C_q^{(n)}(m,k) \neq C_{qs}^{(n)}(m,k)$.

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 consider the matrix-valued generalizations of bipartite tensor product quantum correlations and bipartite infinite-dimensional tensor product quantum correlations, respectively. contribution 0.51 0.28 0.03 unclear 0.64
s1 These sets are denoted by $C_q^{(n)}(m,k)$ and $C_{qs}^{(n)}(m,k)$, respectively, where $m$ is the number of inputs, $k$ is the number of outputs, and $n$ is the matrix size. background 0.81 0.48 0.03 asserted 0.96
s2 We show that, for any $m,k \geq 2$ with $(m,k) \neq (2,2)$, there is an $n \leq 4$ for which we have the separation $C_q^{(n)}(m,k) \neq C_{qs}^{(n)}(m,k)$. result 1.00 0.95 0.91 asserted 1.00

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

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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 the matrix-valued generalizations of bipartite tensor product quantum correlations and bipartite infinite-dimensional tensor product quantum correlations, respectively. These sets are denoted by $C_q^{(n)}(m,k)$ and $C_{qs}^{(n)}(m,k)$, respectively, where $m$ is the number of inputs, $k$ is the number of outputs, and $n$ is the matrix size. We show that, for any $m,k \geq 2$ with $(m,k) \neq (2,2)$, there is an $n \leq 4$ for which we have the separation $C_q^{(n)}(m,k) \neq C_{qs}^{(n)}(m,k)$.

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