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.
The propertyP kBPk ≥B k implies the following equiv- alence:4 Tr(PkB) =Tr(B k)⇐ ⇒P kBPk =B k,(2.45) 4 IfA≥Band Tr(A)≥Tr(B), then Tr(A−B)≥0 forA−B≥0, and this impliesA−B=0
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Localization of quantum states within subspaces
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.