2024/10/29 by Jofre Abellanet-Vidal, Guillem Müller-Rigat, Abellanet-Vidal, Jofre +5 · 2 citations
Engineering · Mathematics · #FOS: Physical sciences #Mathematical Approximation and Integration #Numerical methods in engineering #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2410.22415
openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely unknown. In this work, we employ linear maps and their inverses to derive new sufficient analytical conditions for absolute separability in arbitrary dimensions, providing extremal points of this set and improving its characterization. Additionally, we employ convex geometry optimization to refine the characterization of the set when multiple non-comparable criteria for absolute separability are available. We also address the closely related problem of characterizing the absolute PPT (positive partial transposition) set, which consists of quantum states that remain positive under partial transposition across all unitary transformations. Finally, we extend our results to multipartite states.