2023/06/25 by Michał Banacki, Banacki, Michal · 1 citation
Mathematics · Physics and Astronomy · #81R15 (Primary) 81P40 (Secondary) #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2306.14344
openalex publication_date 2023/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss a scenario of bipartite steering with local subsystems of the parties modeled by certain operator algebras. In particular, we formalize the notion of quantum assemblages in a commuting observables paradigm and focus on equivalent descriptions of such objects providing a systematic analysis of previously scattered approaches. We provide necessary and sufficient conditions for the equivalence of quantum commuting and tensor models that is stable under extensions of the trusted subsystem by arbitrary finite-dimensional ancillae. As a result, we show that the gap between two models of bipartite steering can be observed in an arbitrary scenario with two measurement settings (m = 2) and more than two outcomes (k > 2). We also demonstrate that the identified gap is independent of nonlocality arising from the refutation of Tsirelson's conjecture. Finally, we provide no-go results concerning the possibility of post-quantum steering in this most general bipartite paradigm and discuss related corollaries regarding free probability and operator system approach as well as a link to Tsirelson's problem.