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On Wigdersons' approach to the uncertainty principle

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Nuno Costa Dias, Franz Luef, João Nuno Prata

Functional Analysis · Submitted 29 Dec 2023

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

The authors' main claim We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors.

how it is stated · asserted 0.94 read the record →

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arXiv ID2312.17438 (version 2)
Pith ID26ODZRH4, Pith's permanent record of this paper and its review
CitationFranz Luef, Jo\~ao Nuno Prata, Nuno Costa Dias. "On Wigdersons' approach to the uncertainty principle." arXiv:2312.17438 (2023). https://pith.science/paper/26ODZRH4
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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, 4,930 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.29 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.78 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles.

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 revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. contribution 0.70 0.75 0.04 asserted 0.83
s1 This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. background 0.81 0.08 0.08 asserted 0.99
s2 Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. background 0.68 0.12 0.07 asserted 0.98
s3 Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. background 0.83 0.17 0.07 asserted 0.94
s4 We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. contribution 0.68 0.54 0.53 asserted 0.94
s5 As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles. result 0.94 0.94 0.27 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 0.97.

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  • references and citing sentences
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  • T body sentences
  • C citations
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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 revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles.

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