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Quantum Foundations

Systematic derivation of Tsirelson bounds in arbitrary dimensions

arXiv
Authors: Lorenzo Coccia, Matteo Padovan, Giuseppe Vallone

Year

2026

Paper ID

69941

Status

Preprint

Abstract Read

~2 min

Abstract Words

98

Citations

N/A

Abstract

The study of Bell nonlocality and the bounds of quantum correlations, the so-called Tsirelson bounds, is fundamental to quantum information science and the exploration of the limits of quantum theory. While quantum bounds for qubit systems have been extensively characterized, determining tight quantum bounds for correlations attainable with high-dimensional quantum states and measurements remains a significant challenge. In this work, we propose a systematic derivation of bipartite Tsirelson and local bounds written in terms of sum-of-squares decompositions. Using this method, we discover novel bounds and recover established results for maximally entangled states of qubits and qudits.

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  • This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
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  • The study of Bell nonlocality and the bounds of quantum correlations, the so-called Tsirelson bounds, is fundamental to quantum information science and the exploration of the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2606.21626 [2] arXiv https://arxiv.org/abs/2606.21626 [3] Publisher https://arxiv.org/abs/2606.21626

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