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The condition ran(X)∩ran(Y) =0 requires that∀k x kyk =0

Since the Hermitian operatorsXandYcommute, they share a common spectral decomposition X= n ∑ k=1 xkPk,Y= n ∑ k=1 ykPk,(2

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Localization of quantum states within subspaces

quant-ph · 2026-01-14 · unverdicted · novelty 7.0

Introduces a localization probability lambda for quantum states in subspaces that is stricter than standard overlap Tr(P rho), derived from Schur complement operator decomposition and possessing concavity and super-additivity.

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  • Localization of quantum states within subspaces quant-ph · 2026-01-14 · unverdicted · none · ref 6

    Introduces a localization probability lambda for quantum states in subspaces that is stricter than standard overlap Tr(P rho), derived from Schur complement operator decomposition and possessing concavity and super-additivity.