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arXiv:2310.09047 · International Journal of Theoretical Physics

Insights into Quantum Contextuality and Bell Nonclassicality: a Study on Random Pure Two-Qubit Systems

Giovanni Scala, Antonio Mandarino

Published Jan 12, 2024• 1 citation
arXivHTMLPDF
DOI
10.1007/s10773-023-05543-1

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In a paper, Al-Qasimi [Physics Letters A 449 (2022) 128347] proposed a criterion for contextuality of two-qubit systems extending Peres' proof of contextuality [Phys. Lett. A 151 (1990) 107]. Using this criterion, Al-Qasimi argued that certain discordant states can be contextual even if they are not entangled. Here I demonstrate that Al-Qasimi's criterion does not, in general, imply contextuality of two-qubit system. However, I point out that Al-Qasimi's criterion is related to a different notion of operational nonclassicality of discordant feature, which is inequivalent to contextuality. This nonclassicality beyond contextuality has been formalized in C. Jebarathinam and R. Srikanth [Int. J. Quantum Inf. 23 (2025) 2550037]. Identifying Al-Qasimi's criterion as demonstration of quantum correlation beyond contextuality, it then follows that Al-Qasimi's main conclusion that one cannot equate quantum correlation and discordant feature is made precise.

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In a paper, Al-Qasimi [Physics Letters A 449 (2022) 128347] proposed a criterion for contextuality of two-qubit systems extending Peres' proof of contextuality [Phys. Lett. A 151 (1990) 107]. Using this criterion, Al-Qasimi argued that certain discordant states can be contextual even if they are not entangled. Here I demonstrate that Al-Qasimi's criterion does not, in general, imply contextuality of two-qubit system. However, I point out that Al-Qasimi's criterion is related to a different notion of operational nonclassicality of discordant feature, which is inequivalent to contextuality. This nonclassicality beyond contextuality has been formalized in C. Jebarathinam and R. Srikanth [Int. J. Quantum Inf. 23 (2025) 2550037]. Identifying Al-Qasimi's criterion as demonstration of quantum correlation beyond contextuality, it then follows that Al-Qasimi's main conclusion that one cannot equate quantum correlation and discordant feature is made precise.
Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.
Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by the violation of certain inequalities, the simplest and most important of which are the Clauser-Horne-Shimony-Holt (CHSH) and the Klyachko-Can-Binicioğlu-Shumovski (KCBS), for Bell nonlocality and Kochen-Specker contextuality, respectively. It has been shown that, using the most common interpretation of Bell scenarios, quantum systems cannot violate both inequalities concomitantly, thus suggesting a monogamous relation between the two phenomena. In this Letter, we show that the joint consideration of the CHSH and KCBS inequalities naturally calls for the so-called generalized Bell scenarios, which, contrary to the previous results, allows for joint violation of them. In fact, this result is not a special feature of such inequalities: We provide very strong evidence that there is no monogamy between nonlocality and contextuality in any scenario where both phenomena can be observed. We also implement a photonic experiment to test the synchronous violation of both CHSH and KCBS inequalities. Our results agree with the theoretical predictions, thereby providing experimental proof of the coexistence of Bell nonlocality and contextuality in the simplest scenario, and lead to novel possibilities where both concepts could be jointly employed for quantum information processing protocols.
Contextuality and nonlocality are nonclassical properties exhibited by quantum statistics whose implications profoundly impact both the foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and inequality-free proofs. The former can be understood as the possibility version of contextuality, while the latter refers to proofs of quantum contextuality and nonlocality that are not based on violations of some noncontextuality (or Bell) inequality. By ``possibilistic'' we mean a description in terms of possibilities for the outcomes, which are Boolean variables assuming value one when the corresponding probability is strictly larger than zero and zero otherwise. The present work aims to build a bridge between these two concepts from what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality and nonlocality. As the main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios. Finally, we discuss some interesting consequences arising from the completeness of these possibilistic paradoxes.