Separability of completely symmetric states in a multipartite system
Abstrak
Symmetry plays an important role in the field of quantum mechanics. We consider a subclass of symmetric quantum states in the multipartite system ${N}^{\ensuremath{\bigotimes}d}$, namely, the completely symmetric states, which are invariant under any index permutation. It was hypothesized by L. Qian and D. Chu (arXiv:1810.03125 [quant-ph]) that the completely symmetric states are separable if and only if it is a convex combination of symmetric pure product states. We prove that this conjecture is true for the both bipartite and multipartite cases. Further, we prove that the completely symmetric state $\ensuremath{\rho}$ is separable if its rank is at most 5 or $N+1$. For the states of rank 6 or $N+2$, they are separable if and only if their range contains a product vector. We apply our results to a few widely useful states in quantum information, such as symmetric states, edge states, extreme states, and non-negative states. We also study the relation of completely symmetric states to Hankel and Toeplitz matrices.
Topik & Kata Kunci
Penulis (4)
Lin Chen
D. Chu
Lilong Qian
Yi Shen
Akses Cepat
- Tahun Terbit
- 2018
- Bahasa
- en
- Total Sitasi
- 18×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1103/PhysRevA.99.032312
- Akses
- Open Access ✓