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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23036 |
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| _version_ | 1866910068763525120 |
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| author | Ran, Jiayu |
| author_facet | Ran, Jiayu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23036 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero-Uncertainty States Relative to Observable Algebras Ran, Jiayu Quantum Physics 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. |
| title | Zero-Uncertainty States Relative to Observable Algebras |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.23036 |