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Investigating nonclassicality of many qutrits by symmetric two-qubit operators

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Marcin Markiewicz, Kamil Kostrzewa, Adrian Kolodziejski, Pawel Kurzynski, Wieslaw Laskowski

Quantum Physics · Submitted 30 Jun 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that this procedure partially resolves the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations.

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arXiv ID1606.09603 (version 1)
Pith IDUIT5PEUS, Pith's permanent record of this paper and its review
CitationAdrian Kolodziejski, Kamil Kostrzewa, Marcin Markiewicz, Pawel Kurzynski, Wieslaw Laskowski. "Investigating nonclassicality of many qutrits by symmetric two-qubit operators." arXiv:1606.09603 (2016). https://pith.science/paper/UIT5PEUS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,020 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.80 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We introduce a new method of investigating qutrit nonclassicality by translating qutrit operators to symmetric two-qubit operators. We show that this procedure partially resolves the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations. Namely we express Bell operators corresponding to qutrit Bell inequalities in terms of symmetric two-qubit operators, and analyze the maximal quantum violation of a given Bell inequality from the qubit perspective. As an example we show that the two-qutrit CGLMP(Collins-Gisin-Linden-Massar-Popescu) Bell inequality can be seen as a combination of Mermin's and CHSH (Clauser-Horne-Shimony-Holt) qubit Bell inequalities, and therefore the optimal state violating this combination differs from the one which corresponds to the maximally entangled state of two qutrits. In addition, we discuss the same problem for a three qutrit inequality. We also demonstrate that the maximal quantum violation of the CGLMP inequality follows from complementarity of correlations.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce a new method of investigating qutrit nonclassicality by translating qutrit operators to symmetric two-qubit operators. contribution 0.62 0.94 0.13 asserted 1.00
s1 We show that this procedure partially resolves the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations. result 0.72 0.93 0.48 asserted 0.95
s2 Namely we express Bell operators corresponding to qutrit Bell inequalities in terms of symmetric two-qubit operators, and analyze the maximal quantum violation of a given Bell inequality from the qubit perspective. method 0.84 0.93 0.16 asserted 0.99
s3 As an example we show that the two-qutrit CGLMP(Collins-Gisin-Linden-Massar-Popescu) Bell inequality can be seen as a combination of Mermin's and CHSH (Clauser-Horne-Shimony-Holt) qubit Bell inequalities, and therefore the optimal state violating this combination differs from the one which corresponds to the maximally entangled state of two qutrits. result 0.89 0.88 0.24 asserted 1.00
s4 In addition, we discuss the same problem for a three qutrit inequality. contribution 1.00 0.83 0.05 asserted 0.85
s5 We also demonstrate that the maximal quantum violation of the CGLMP inequality follows from complementarity of correlations. result 0.77 0.90 0.17 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 0.99.

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Original abstract

We introduce a new method of investigating qutrit nonclassicality by translating qutrit operators to symmetric two-qubit operators. We show that this procedure partially resolves the discrepancy between maximal qutrit entanglement and maximal nonclassicality of qutrit correlations. Namely we express Bell operators corresponding to qutrit Bell inequalities in terms of symmetric two-qubit operators, and analyze the maximal quantum violation of a given Bell inequality from the qubit perspective. As an example we show that the two-qutrit CGLMP(Collins-Gisin-Linden-Massar-Popescu) Bell inequality can be seen as a combination of Mermin's and CHSH (Clauser-Horne-Shimony-Holt) qubit Bell inequalities, and therefore the optimal state violating this combination differs from the one which corresponds to the maximally entangled state of two qutrits. In addition, we discuss the same problem for a three qutrit inequality. We also demonstrate that the maximal quantum violation of the CGLMP inequality follows from complementarity of correlations.

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