Zero-Uncertainty States Relative to Observable Algebras

• URL: http://arxiv.org/abs/2603.23036v1
• Date: Tue, 24 Mar 2026 10:13:17 GMT
• Title: Zero-Uncertainty States Relative to Observable Algebras
• Abstract summary: We study zero-uncertainty states with quantum memory from an operator-algebraic perspective.<n>We prove a rigidity theorem for purity and maximal entanglement.<n>We present an example from quantum steering to illustrate how our framework helps resolve a concrete physical question.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study zero-uncertainty states with quantum memory from an operator-algebraic perspective, which naturally accommodates degenerate projective-valued measurements. In the equal-dimension setting, we prove a rigidity theorem for purity and maximal entanglement. We then analyze two mechanisms by which this rigidity can fail: one arising from proper observable subalgebras, and the other from allowing larger memory dimensions. In these cases, we give corresponding algebraic decomposition and representation-theoretic descriptions, and compare their mathematical structure with their physical interpretation. Finally, we present an example from quantum steering to illustrate how our framework helps resolve a concrete physical question in a specific setting.

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