An Effective Way to Determine the Separability of Quantum State

Ma-Cheng Yang; Cong-Feng Qiao

doi:10.22331/q-2025-05-06-1734

An Effective Way to Determine the Separability of Quantum State

¹School of Physical Sciences, University of Chinese Academy of Sciences, YuQuan Road 19A, Beijing 100049, China
²Key Laboratory of Vacuum Physics, CAS, YuQuan Road 19A, Beijing 100049, China

Published:	2025-05-06, volume 9, page 1734
Editor:	Jens Siewert
Eprint:	arXiv:2403.07351v2
Doi:	https://doi.org/10.22331/q-2025-05-06-1734
Citation:	Quantum 9, 1734 (2025).

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Abstract

We propose in this work a practical approach to address the longstanding and challenging problem of quantum separability, leveraging the correlation matrices of generic observables. General separability conditions are obtained by dint of constructing the measurement-induced Bloch space, which in essence come from the intrinsic constraints in the space of quantum state. The novel approach can not only reproduce various established entanglement criteria, it may as well brings about some new results, possessing obvious advantages for certain bound entangled states and the high dimensional Werner states. Moreover, it is found that criteria obtained in our approach can be directly transformed into entanglement witness operators.

Featured image: Entanglement detection for UPB bound entangled states with white noise $\rho_{\mathrm{UPB}}(p)$ and chessboard states $\rho_{\mathrm{CB}}$.

Popular summary

Entanglement serves as a fundamental resource for various quantum information tasks and underpins the non-local features of quantum mechanics. Developing experimentally operational criteria is crucial for understanding the nature of entanglement and expanding its potential applications in quantum information. In this work, we establish a novel connection between the geometry of measurement-induced Bloch space and the separability problem, leading to a comprehensive framework for constructing separability criteria. This innovative approach not only reproduces several established entanglement criteria but also yields new results, demonstrating clear advantages for certain bound entangled states and high-dimensional Werner states. Furthermore, the new criteria can be transformed into entanglement witness operators, enhancing the transparency of constructing entanglement witnesses from generic observables.

► BibTeX data

@article{Yang2025effectivewayto,
  doi = {10.22331/q-2025-05-06-1734},
  url = {https://doi.org/10.22331/q-2025-05-06-1734},
  title = {An {E}ffective {W}ay to {D}etermine the {S}eparability of {Q}uantum {S}tate},
  author = {Yang, Ma-Cheng and Qiao, Cong-Feng},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1734},
  month = may,
  year = {2025}
}

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