No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917892303355904 |
|---|---|
| author | Frembs, Markus Okay, Cihan Chung, Ho Yiu |
| author_facet | Frembs, Markus Okay, Cihan Chung, Ho Yiu |
| contents | 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, [J. Phys. A, 53, 385304 (2020)] 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14018 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords Frembs, Markus Okay, Cihan Chung, Ho Yiu Quantum Physics 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, [J. Phys. A, 53, 385304 (2020)] 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. |
| title | No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2209.14018 |