Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State

• URL: http://arxiv.org/abs/2604.04816v1
• Date: Mon, 06 Apr 2026 16:20:54 GMT
• Title: Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State
• Abstract summary: Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle.<n>We show that contextuality is governed solely by a population parameter $pangle$, associated with the occupation of the qutrit subsystem in the $|2rangle level.<n>In contrast, nonlocality depends irreducibly on coherence, involving both amplitudes and phases encoded in parameters $(X_i, Y_i)$.
• Score: 21.854308474027224
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle. In a hybrid CHSH--KCBS scenario involving the entanglment of a qubit and a qutrit, the qutrit supports the KCBS contextuality test, and the CHSH nonlocality arises from correlations between the qubit and qutrit. Here, we derive the analytical closed-form expressions for both inequalities and also simulate this physics on a quantum circuit. We show that contextuality is governed solely by a population parameter $p_2$, associated with the occupation of the qutrit subsystem in the $|2\rangle$ level, which plays a distinguished role in the KCBS structure. In contrast, nonlocality depends irreducibly on coherence, involving both amplitudes and phases encoded in parameters $(X_i, Y_i)$. This separation of physical resources reveals parameter regimes that optimize KCBS violation while suppress CHSH violation, and vice versa. As a result, the optimal regions do not overlap, and coexistence is restricted to a narrow intermediate regime in parameter space.

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