bibkey: chenchuqianshen2019cs
authors: Lin Chen; Delin Chu; Lilong Qian; Yi Shen
year: 2019
title: "Separability of completely symmetric states in a multipartite system"
doi: 10.1103/PhysRevA.99.032312
url: https://arxiv.org/abs/1812.04182v4
claim: "A state on (C^N)^{⊗d} is completely symmetric when its entries are invariant under every permutation of the 2d index positions; the paper shows that multi-qubit and two-qutrit completely symmetric states are separable and asks whether multi-qutrit completely symmetric states are separable."
strata_touched:
  - D5/S3/Quantum/Entanglement/Witness/ThreeQutritCompletelySymmetricEntangled
license: citation-only
triage: anchor

Chen, Chu, Qian and Shen, Separability of completely symmetric states in a multipartite system

L. Chen, D. Chu, L. Qian and Y. Shen, Phys. Rev. A 99, 032312 (2019); arXiv:1812.04182v4. Quotations are from the v4 TeX source.

A state is separable if it is a convex combination of pure product states. Writing a state on $({\mathbb{C}}^N{)}^{\otimes d}$ as $\rho ={\sum }_{I,J}{\rho }_{I,J}|I⟩⟨J|$ with multi-indices $I,J$, the state is completely symmetric when ${\rho }_{\pi (I,J)}={\rho }_{I,J}$ for every permutation $\pi$ of the $2d$ index positions; in the multipartite system, separable means fully separable. The Conclusion lists among the future problems:

Are multi-qutrit CS states separable?

Verified locator

Source: https://arxiv.org/abs/1812.04182v4

• DOI: https://doi.org/10.1103/PhysRevA.99.032312 (Physical Review A 99(3), article 032312; title, authors, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/1812.04182v4. The e-print, a single gzip-compressed file CSv2.tex, has 2357 lines and md5 52f01e75f543a97d43fc560e5af4a8d8. Locations:
  • separability, l. 244–252; complete symmetry, l. 360–391; full separability, l. 444–452;
  • the question, l. 1857.