Systematic derivation of Tsirelson bounds in arbitrary dimensions

• URL: http://arxiv.org/abs/2606.21626v1
• Date: Fri, 19 Jun 2026 17:30:44 GMT
• Title: Systematic derivation of Tsirelson bounds in arbitrary dimensions
• Abstract summary: The study of Bell nonlocality and the bounds of quantum correlations is fundamental to quantum information science.<n>We propose a systematic derivation of bipartite Tsirelson and local bounds written in terms of sum-of-squares decompositions.
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• License: http://creativecommons.org/licenses/by/4.0/
• 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 qu$d$its.

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