Linear transformations of quantum states

S. Croke, S.M. Barnett, S. Stenholm

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper considers the most general linear transformation of a quantum state. We enumerate the conditions necessary to retain a physical interpretation of the transformed state: hermeticity, normalization and complete positivity. We show that these can be formulated in terms of an associated transformation introduced by Choi in 1975. We extend his treatment and display the mathematical argumentation in a manner closer to that used in traditional quantum physics. We contend that our approach displays the implications of the physical requirements in a simple and intuitive way. In addition, defining an arbitrary vector, we may derive a probability distribution over the spectrum of the associated transformation. This fixes the average of the eigenvalue independently of the vector chosen. The formal results are illustrated by a couple of examples.
Original languageEnglish
Pages (from-to)893-906
Number of pages13
JournalAnnals of Physics
Issue number4
Publication statusPublished - Apr 2008


  • linear transformations
  • complete positivity
  • Kraus sum

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