An Unentangled Gleason's Theorem

Nolan R. Wallach

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An Unentangled Gleason's Theorem

Nolan R. Wallach

Quantum Physics · Submitted 22 Feb 2000

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

The authors' main claim The purpose of this note is to give a generalization of Gleason's theorem inspired by recent work in quantum information theory on "nonlocality without entanglement." For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,343 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.93 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.47 · 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.

The purpose of this note is to give a generalization of Gleason's theorem inspired by recent work in quantum information theory on "nonlocality without entanglement." For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule. However, if one system is of dimension 2 this is not necessarily the case.

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	The purpose of this note is to give a generalization of Gleason's theorem inspired by recent work in quantum information theory on "nonlocality without entanglement." For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule.	result 0.67	0.85	0.93	asserted 1.00
s1	However, if one system is of dimension 2 this is not necessarily the case.	limitation 0.89	0.54	0.07	hedged possibility 0.55

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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arXiv listing abstract v1

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full text
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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

The purpose of this note is to give a generalization of Gleason's theorem inspired by recent work in quantum information theory on "nonlocality without entanglement." For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule. However, if one system is of dimension 2 this is not necessarily the case.

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References

How the literature uses it

9 arXiv papers cite this in 13 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 · 11 sentences without a confident label

Compares with it 1 paper

The difference is that [ref] considers global sections of the undilated probabilistic presheaf $(V_1& 2)$ in Def.

Contextuality and the fundamental theorems of quantum mechanics · The Bell presheaf and reformulation of Bell's theorem · 0.97

Cites it as background 1 paper

Gleason's theorem.– We investigate the class of locally quantum theories studied in a series of works in the recent past [ref] .

Certifying beyond quantumness of locally quantum no-signalling theories through quantum input Bell test · Introduction · 0.98

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