Multi-Unitary Complex Hadamard Matrices
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_ | 1866913391469133824 |
|---|---|
| author | Bruzda, Wojciech Rajchel-Mieldzioć, Grzegorz Życzkowski, Karol |
| author_facet | Bruzda, Wojciech Rajchel-Mieldzioć, Grzegorz Życzkowski, Karol |
| contents | We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of complex Hadamard matrices of order $N=d^k$. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ($H=H^{\rm R}$ or $H=H^{\rmΓ}$), two-unitary ($H^R$ and $H^Γ$ are unitary), or $k$-unitary. Here $X^{\rm R}$ denotes reshuffling of a matrix $X$ describing a bipartite system, and $X^{\rm Γ}$ its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in $1+1$ dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00999 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-Unitary Complex Hadamard Matrices Bruzda, Wojciech Rajchel-Mieldzioć, Grzegorz Życzkowski, Karol Quantum Physics Mathematical Physics 05B20, 51F25, 46N50 We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of complex Hadamard matrices of order $N=d^k$. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ($H=H^{\rm R}$ or $H=H^{\rmΓ}$), two-unitary ($H^R$ and $H^Γ$ are unitary), or $k$-unitary. Here $X^{\rm R}$ denotes reshuffling of a matrix $X$ describing a bipartite system, and $X^{\rm Γ}$ its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in $1+1$ dimensions. |
| title | Multi-Unitary Complex Hadamard Matrices |
| topic | Quantum Physics Mathematical Physics 05B20, 51F25, 46N50 |
| url | https://arxiv.org/abs/2306.00999 |