Localization of quantum states within subspaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917508286513152 |
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| author | Salcedo, L. L. |
| author_facet | Salcedo, L. L. |
| contents | This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator supported inside the chosen subspace and C has support disjoint from it. The localized component B can be expressed via the Schur complement and characterized through an A-dependent inner product and suitable trace inequalities. For quantum states, this yields a probability lambda that a state rho be completely contained in a subspace, which is strictly more restrictive than the usual overlap probability Tr(P rho) and enjoys concavity and super-additivity properties. The resulting framework admits natural interpretations in quantum information, including entropic aspects and a simple cryptographic masking scheme based on the uniqueness of the decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09817 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Localization of quantum states within subspaces Salcedo, L. L. Quantum Physics Mathematical Physics This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator supported inside the chosen subspace and C has support disjoint from it. The localized component B can be expressed via the Schur complement and characterized through an A-dependent inner product and suitable trace inequalities. For quantum states, this yields a probability lambda that a state rho be completely contained in a subspace, which is strictly more restrictive than the usual overlap probability Tr(P rho) and enjoys concavity and super-additivity properties. The resulting framework admits natural interpretations in quantum information, including entropic aspects and a simple cryptographic masking scheme based on the uniqueness of the decomposition. |
| title | Localization of quantum states within subspaces |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2601.09817 |