On discrete Wigner transforms
| dc.contributor.author | Cai, Zhenning | |
| dc.contributor.author | Lu, Jianfeng | |
| dc.contributor.author | Stubbs, Kevin | |
| dc.date.accessioned | 2018-12-19T14:07:05Z | |
| dc.date.available | 2018-12-19T14:07:05Z | |
| dc.date.updated | 2018-12-19T14:07:04Z | |
| dc.description.abstract | In this work, we derive a discrete analog of the Wigner transform over the space $(\mathbb{C}^p)^{\otimes N}$ for any prime $p$ and any positive integer $N$. We show that the Wigner transform over this space can be constructed as the inverse Fourier transform of the standard Pauli matrices for $p=2$ or more generally of the Heisenberg-Weyl group elements for $p > 2$. We connect our work to a previous construction by Wootters of a discrete Wigner transform by showing that for all $p$, Wootters' construction corresponds to taking the inverse symplectic Fourier transform instead of the inverse Fourier transform. Finally, we discuss some implications of these results for the numerical simulation of many-body quantum spin systems. | |
| dc.identifier.uri | ||
| dc.subject | math-ph | |
| dc.subject | math-ph | |
| dc.subject | math.MP | |
| dc.title | On discrete Wigner transforms | |
| dc.type | Journal article | |
| duke.contributor.orcid | Lu, Jianfeng|0000-0001-6255-5165 | |
| duke.contributor.orcid | Stubbs, Kevin|0000-0003-0062-5097 | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.organisational-group | Duke | |
| pubs.organisational-group | Chemistry | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Physics | |
| pubs.organisational-group | Student |