| Integration with Respect to Operator-Valued Measures with Applications to Quantum Estimation Theory (2007) | |||||||||||
Abstract | |||||||||||
| The problem of quantum measurement has received a great deal of attention in recent years, both in the quantum physics literature and in the context of optical communications. An account of these ideas may be found in Davies [1976] and Holevo [1973]. The development of a theory of quantum estimation requires a theory of integration with respect to operator-valued measures. Indeed, Holevo [1973] in his investigations on the Statistical Decision Theory for Quantum Systems develops such a theory which, however, is more akin to Riemann Integration. The objective of this paper is to develop a theory which is analogous to Lebesque integration and which is natural in the context of quantum physics problems and show how this can be applied to quantum estimation problems. The theory that we present has little overlap with the theory of integration with respect to vector measures nor the integration theory developed by Thomas [1970].. Additional contract no. ENG-76-02860. Prepared in cooperation with Science Applications, Inc., McLean, VA. | |||||||||||
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