Instruments and mutual entropies in quantum information

Tom 73 / 2006

Alberto Barchielli, Giancarlo Lupieri Banach Center Publications 73 (2006), 65-80 MSC: Primary 81P15; Secondary 94A17. DOI: 10.4064/bc73-0-4


General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a posteriori state as output. Then, by using mutual entropies on von Neumann algebras and the identification of instruments and channels, many old and new informational inequalities are obtained in a unified manner. Such inequalities involve various quantities which characterize the performances of the instrument under study; in particular, these inequalities include and generalize the famous Holevo's bound.


  • Alberto BarchielliPolitecnico di Milano
    Dipartimento di Matematica
    Piazza Leonardo da Vinci 32
    I-20133 Milano, Italy
  • Giancarlo LupieriUniversità degli Studi di Milano
    Dipartimento di Fisica
    Via Celoria 16
    I-20133 Milano, Italy

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