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On steering in the C*-algebraic framework
Michal Banac · 2026-05-25 · via math updates on arXiv.org

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Abstract: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.
Comments: 18 pages, added section 7 and Thm. 4.6, Cor. 4.9, Prop. 6.3, Cor. 8.3, Cor. 9.3
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)
MSC classes: 81R15 (Primary) 81P40 (Secondary)
Cite as: arXiv:2306.14344 [quant-ph]
  (or arXiv:2306.14344v4 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.2306.14344

arXiv-issued DOI via DataCite

Submission history

From: Michał Banacki [view email]
[v1] Sun, 25 Jun 2023 21:15:12 UTC (16 KB)
[v2] Thu, 3 Aug 2023 14:39:45 UTC (18 KB)
[v3] Tue, 17 Jun 2025 17:49:11 UTC (21 KB)
[v4] Fri, 22 May 2026 15:19:49 UTC (24 KB)