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Sufficient criteria for absolute separability in arbitrary dimensions via linear map inverses.

Jofre Abellanet Vidal1, Guillem Müller-Rigat2, Grzegorz Rajchel-Mieldzioć2,3

  • 1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain.

Reports on Progress in Physics. Physical Society (Great Britain)
|September 29, 2025
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Summary

This study introduces new analytical conditions to better characterize absolutely separable quantum states and their properties. These findings advance our understanding of quantum states that resist entanglement under global transformations.

Keywords:
absolute PPTabsolute separabilityquantum entanglementquantum mapssymmetric states

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Area of Science:

  • Quantum Information Theory
  • Mathematical Physics
  • Quantum Computing

Background:

  • Absolutely separable quantum states are crucial for quantum information processing but their characterization remains incomplete.
  • Understanding these states is key to identifying robust quantum resources.

Purpose of the Study:

  • To derive novel analytical conditions for identifying absolutely separable quantum states.
  • To improve the characterization of the set of absolutely separable states using convex geometry.
  • To extend these findings to multipartite quantum systems and the absolute positive partial transposition set.

Main Methods:

  • Utilizing linear maps and their inverses to establish sufficient conditions for absolute separability.
  • Employing convex geometry optimization for refining state characterization.
  • Applying derived methods to multipartite states and the absolute positive partial transposition set.

Main Results:

  • New sufficient analytical conditions for absolute separability in arbitrary dimensions were derived.
  • Extremal points of the absolutely separable set were identified, enhancing its characterization.
  • The study successfully extended the analysis to multipartite states and the absolute PPT set.

Conclusions:

  • The derived conditions provide significant advancements in characterizing absolutely separable and absolute PPT quantum states.
  • The work offers new tools for analyzing quantum correlations and their robustness.
  • This research contributes to a deeper theoretical foundation for quantum information science.