Linear transformations of quantum states

Croke, S. and Barnett, S.M. and Stenholm, S. (2008) Linear transformations of quantum states. Annals of Physics, 323 (4). pp. 893-906. ISSN 0003-4916 (http://dx.doi.org/10.1016/j.aop.2007.06.001)

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Abstract

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.

  • Item type:Article
    ID code:19704
    Dates:
    Date
    Event
    April 2008
    Published
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Strathprints Administrator
    Date deposited:19 May 2010 17:21
    Last modified:11 Nov 2024 09:21
    URI:https://strathprints.strath.ac.uk/id/eprint/19704
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