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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.15607 |
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| _version_ | 1866914164486701056 |
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| author | Fiorentino, Vincenzo Weigert, Stefan |
| author_facet | Fiorentino, Vincenzo Weigert, Stefan |
| contents | We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$ from a simple requirement: the probabilities assigned to measurement outcomes must not depend on whether a system is considered on its own or as a subsystem of a larger one. In line with Gleason's original theorem, our approach assigns probabilities only to projection-valued measures, while other known extensions rely on considering more general classes of measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gleason's Theorem for a Qubit as Part of a Composite System Fiorentino, Vincenzo Weigert, Stefan Quantum Physics We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$ from a simple requirement: the probabilities assigned to measurement outcomes must not depend on whether a system is considered on its own or as a subsystem of a larger one. In line with Gleason's original theorem, our approach assigns probabilities only to projection-valued measures, while other known extensions rely on considering more general classes of measurements. |
| title | Gleason's Theorem for a Qubit as Part of a Composite System |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.15607 |