Schmidt number for density matrices

Barbara M. Terhal*, Paweł Horodecki

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

246 Citations (Scopus)


We introduce the notion of a Schmidt number of a bipartite density matrix. We show that k-positive maps witness the Schmidt number, in the same way that positive maps witness entanglement. We determine the Schmidt number of the family of states that is made from mixing the completely mixed state and a maximally entangled state. We show that the Schmidt number does not necessarily increase when taking tensor copies of a density matrix ρ; we give an example of a density matrix for which the Schmidt numbers of ρ and ρ⊗ρ are both 2.

Original languageEnglish
Article number040301
Pages (from-to)403011-403014
Number of pages4
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
Publication statusPublished - 2000
Externally publishedYes

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