Qubits as Hypermatrices and Entanglement
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916204120113152 |
|---|---|
| author | Dobes, Isaac Jing, Naihuan |
| author_facet | Dobes, Isaac Jing, Naihuan |
| contents | In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $π$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06944 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Qubits as Hypermatrices and Entanglement Dobes, Isaac Jing, Naihuan Quantum Physics Mathematical Physics In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $π$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle. |
| title | Qubits as Hypermatrices and Entanglement |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2312.06944 |