Interpreting symplectic linear transformations in a two-qubit phase space
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909374863114240 |
|---|---|
| author | Wootters, William K. |
| author_facet | Wootters, William K. |
| contents | For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on the state. That is, performing this unitary transformation is simply a matter of moving Wigner-function values around in phase space. This result holds in particular for the simplest discrete Wigner function defined on a $d \times d$ phase space when the Hilbert-space dimension $d$ is odd. It does not hold for a $d \times d$ phase space if the dimension is even. Here we show, though, that a generalized version of this correspondence does apply in the case of a two-qubit phase space. In this case, a symplectic linear permutation of the points of the phase space, together with a certain reinterpretation of the Wigner function, is equivalent to a unitary transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09922 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpreting symplectic linear transformations in a two-qubit phase space Wootters, William K. Quantum Physics For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on the state. That is, performing this unitary transformation is simply a matter of moving Wigner-function values around in phase space. This result holds in particular for the simplest discrete Wigner function defined on a $d \times d$ phase space when the Hilbert-space dimension $d$ is odd. It does not hold for a $d \times d$ phase space if the dimension is even. Here we show, though, that a generalized version of this correspondence does apply in the case of a two-qubit phase space. In this case, a symplectic linear permutation of the points of the phase space, together with a certain reinterpretation of the Wigner function, is equivalent to a unitary transformation. |
| title | Interpreting symplectic linear transformations in a two-qubit phase space |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.09922 |