Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910105922961408 |
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| author | Nguyen, Khai Doan, Duc M. Nguyen, Hung Q. |
| author_facet | Nguyen, Khai Doan, Duc M. Nguyen, Hung Q. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State Nguyen, Khai Doan, Duc M. Nguyen, Hung Q. Quantum Physics 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. |
| title | Coexistence of CHSH Nonlocality and KCBS Contextuality in a Single Quantum State |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.04816 |