xii, 133 p. : ill. (some col.) / We study entanglement estimation and verification in realistic situations, taking into account experimental imperfections and statistical fluctuations due to finite data. We consider both photonic and spin-1/2 systems. We study how entanglement created with mixed photon wave packets is degraded. We apply statistical analysis to and propose criteria for reliable entanglement verification and estimation. Finally we devote some effort to making quantum state estimation efficient by applying information criteria. This dissertation includes previously published co-authored material. / Committee in charge: Michael G. Raymer, Chair; Steven J. van Enk, Advisor; Stephen Hs,u Member; Jens U. Noeckel, Member; Je rey A. Cina, Outside Member;