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Main Author: Salcedo, L. L.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.09817
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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