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Extreme affine transformations

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Abstract

We classify the extreme points of the compact convex set of affine maps of IRn which map into itself the closed unit ball. This work is a preliminary step towards solving the problem of finding the extreme points of the compact convex set of affine maps of theN×N density matrices (dynamical maps of anN-level system) and forn=3 furnishes the solution of the problem in the simplest case of a two-level system.

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Authors and Affiliations

  1. Istituto di Fisica dell'Università, I-20133, Milano, Italy

    Vittorio Gorini

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Milano, Italy

    Vittorio Gorini

  3. Department of Physics, Center for Particle Theory, The University of Texas, 78712, Austin, Texas, USA

    E. C. G. Sudarshan

  4. Centre for Theoretical Studies, Indian Institute of Science, 560012, Bangalore, India

    E. C. G. Sudarshan

Authors
  1. Vittorio Gorini
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  2. E. C. G. Sudarshan
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Additional information

Communicated by H. Araki

The bulk of this work was performed while the first author was visiting the Center for Particle Theory of the University of Texas at Austin under the partial support of the U.S.A.E.C. under contract ORO-(40-1) 3992. A travel grant under the Fulbright-Hays program is acknowledged.

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Gorini, V., Sudarshan, E.C.G. Extreme affine transformations. Commun.Math. Phys. 46, 43–52 (1976). https://doi.org/10.1007/BF01610499

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  • DOI: https://doi.org/10.1007/BF01610499

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