dorsal/arxiv
View SchemaThe wanted extension of Fujii and Tsurumaru's formula for the spectral radius of the Bell-CHSH operator
| Authors | Albrecht Böttcher, Ilya M. Spitkovsky |
|---|---|
| Categories | |
| ArXiv ID | 2601.09392vv1 |
| URL | https://arxiv.org/abs/2601.09392 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
This paper is motivated by a recent paper of Yuki Fujii and Toyohiro Tsurumaru in which they established a beautiful formula for the spectral radius of the Bell-CHSH operator on finite-dimensional Hilbert spaces. To tackle the operator on infinite-dimensional spaces, they elaborated a method based on appropriate approximation of commutators of infinite-dimensional orthogonal projections by commutators of orthogonal projections on finite-dimensional spaces. We here give a proof of Fujii and Tsurumaru's original formula that works in all dimensions. We also simplify and correct some arguments employed by Fujii and Tsurumaru.
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"date_created": "2026-02-17T05:53:19.906000Z",
"date_modified": "2026-02-17T05:53:19.906000Z",
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"abstract": "This paper is motivated by a recent paper\n of Yuki Fujii and Toyohiro Tsurumaru in which they established a beautiful formula\n for the spectral radius of the Bell-CHSH operator on finite-dimensional Hilbert spaces.\n To tackle the operator on infinite-dimensional spaces, they elaborated a method based\n on appropriate approximation of commutators of infinite-dimensional orthogonal projections by\n commutators of orthogonal projections on finite-dimensional spaces. We here give a proof of\n Fujii and Tsurumaru\u0027s original formula that works in all dimensions. We also simplify and correct\n some arguments employed by Fujii and Tsurumaru.",
"arxiv_id": "2601.09392",
"authors": [
"Albrecht B\u00f6ttcher",
"Ilya M. Spitkovsky"
],
"categories": [
"math.FA"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "The wanted extension of Fujii and Tsurumaru\u0027s formula for the spectral radius of the Bell-CHSH operator",
"url": "https://arxiv.org/abs/2601.09392",
"version": "v1"
},
"schema_id": "dorsal/arxiv",
"source": {
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"id": "arXiv Dataset",
"type": "Model",
"variant": "snapshot-2026-01-17",
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