No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular,...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-01-08-1583/pdf/ |
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| author | Markus Frembs Cihan Okay Ho Yiu Chung |
| author_facet | Markus Frembs Cihan Okay Ho Yiu Chung |
| author_sort | Markus Frembs |
| collection | DOAJ |
| description | Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular, it is not known whether there exist LCS in odd dimension, which admit finite-dimensional quantum, but no classical solutions. In recent work, \cite{QassimWallman2020} have shown that unlike in the Boolean case, where the $n$-qubit Pauli group gives rise to quantum solutions of LCS such as the Mermin-Peres square, the n-qudit Pauli group never gives rise to quantum solutions of a LCS in odd dimension. Here, we generalise this result towards the Clifford hierarchy. More precisely, we consider tensor products of groups generated by (single-qudit) Pauli and diagonal Clifford operators. |
| format | Article |
| id | doaj-art-dd1064c919774caf835363a0a05029db |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-dd1064c919774caf835363a0a05029db2025-01-08T17:19:57ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-01-019158310.22331/q-2025-01-08-158310.22331/q-2025-01-08-1583No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal CliffordsMarkus FrembsCihan OkayHo Yiu ChungLinear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular, it is not known whether there exist LCS in odd dimension, which admit finite-dimensional quantum, but no classical solutions. In recent work, \cite{QassimWallman2020} have shown that unlike in the Boolean case, where the $n$-qubit Pauli group gives rise to quantum solutions of LCS such as the Mermin-Peres square, the n-qudit Pauli group never gives rise to quantum solutions of a LCS in odd dimension. Here, we generalise this result towards the Clifford hierarchy. More precisely, we consider tensor products of groups generated by (single-qudit) Pauli and diagonal Clifford operators.https://quantum-journal.org/papers/q-2025-01-08-1583/pdf/ |
| spellingShingle | Markus Frembs Cihan Okay Ho Yiu Chung No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords Quantum |
| title | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords |
| title_full | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords |
| title_fullStr | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords |
| title_full_unstemmed | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords |
| title_short | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords |
| title_sort | no quantum solutions to linear constraint systems in odd dimension from pauli group and diagonal cliffords |
| url | https://quantum-journal.org/papers/q-2025-01-08-1583/pdf/ |
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