On steering in the C*-algebraic framework

• URL: http://arxiv.org/abs/2306.14344v3
• Date: Tue, 17 Jun 2025 17:49:11 GMT
• Title: On steering in the C*-algebraic framework
• Authors: Michal Banacki,
• Abstract summary: We formalize the notion of quantum assemblages in a commuting observables paradigm.<n>We show that the gap between two models of bipartite steering can be observed in an arbitrary scenario.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 ($k > 2$). 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.

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