Classifying the simplest Bell inequalities beyond qubits and their applications towards self-testing

• URL: http://arxiv.org/abs/2602.08469v1
• Date: Mon, 09 Feb 2026 10:16:02 GMT
• Title: Classifying the simplest Bell inequalities beyond qubits and their applications towards self-testing
• Authors: Palash Pandya, Shubhayan Sarkar, Remigiusz Augusiak,
• Abstract summary: Bell inequalities show gap between local and nonlocal quantum behaviour.<n>This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory.<n>It provides a systematic way to construct Bell inequalities tailored to specific quantum information processing tasks.
• Score: 0.22399170518036918
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest $(2,2,2)$ scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the $(2,2,3)$ scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.

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