Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914955546066944 |
|---|---|
| author | Płodzień, Marcin Chwedeńczuk, Jan Lewenstein, Maciej Rajchel-Mieldzioć, Grzegorz |
| author_facet | Płodzień, Marcin Chwedeńczuk, Jan Lewenstein, Maciej Rajchel-Mieldzioć, Grzegorz |
| contents | Many-body quantum systems can be characterised using the notions of \emph{k}-separability and entanglement depth. A quantum state is \emph{k}-separable if it can be expressed as a mixture of \emph{k} entangled subsystems, and its entanglement depth is given by the size of the largest entangled subsystem. In this paper we propose a multipartite entanglement measure that satisfies the following criteria: (i) it can be used with both pure and mixed states; (ii) it is encoded in a single element of the density matrix, so it does not require knowledge of the full spectrum of the density matrix; (iii) it can be applied to large systems; and (iv) it can be experimentally verified. The proposed method allows the certification of \emph{non-k}-separability of a given quantum state. We show that the proposed method successfully classifies three-qubit systems into known stochastic local operations and classical communication (SLOCC) classes, namely bipartite, \mbox{W-,} and GHZ-type entanglement. Furthermore, we characterise the \emph{non-k}-separability in known nine SLOCC classes of four-qubit states, absolutely maximally entangled states for five and six qubits and for arbitrary size qubit Dicke states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity Płodzień, Marcin Chwedeńczuk, Jan Lewenstein, Maciej Rajchel-Mieldzioć, Grzegorz Quantum Physics Quantum Gases Many-body quantum systems can be characterised using the notions of \emph{k}-separability and entanglement depth. A quantum state is \emph{k}-separable if it can be expressed as a mixture of \emph{k} entangled subsystems, and its entanglement depth is given by the size of the largest entangled subsystem. In this paper we propose a multipartite entanglement measure that satisfies the following criteria: (i) it can be used with both pure and mixed states; (ii) it is encoded in a single element of the density matrix, so it does not require knowledge of the full spectrum of the density matrix; (iii) it can be applied to large systems; and (iv) it can be experimentally verified. The proposed method allows the certification of \emph{non-k}-separability of a given quantum state. We show that the proposed method successfully classifies three-qubit systems into known stochastic local operations and classical communication (SLOCC) classes, namely bipartite, \mbox{W-,} and GHZ-type entanglement. Furthermore, we characterise the \emph{non-k}-separability in known nine SLOCC classes of four-qubit states, absolutely maximally entangled states for five and six qubits and for arbitrary size qubit Dicke states. |
| title | Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2406.10662 |