Abstract
A partial ordering in the class of observables (∼ positive operator-valued measures, introduced by Davies and by Ludwig) is explored. The ordering is interpreted as a form of nonideality, and it allows one to compare ideal and nonideal versions of the same observable. Optimality is defined as maximality in the sense of the ordering. The framework gives a generalization of the usual (implicit) definition of self-adjoint operators as optimal observables (von Neumann), but it can, in contrast to this latter definition, be justified operationally. The nonideality notion is compared to other quantum estimation theoretic methods. Measures for the amount of nonideality are derived from information theory.
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Martens, H., de Muynck, W.M. Nonideal quantum measurements. Found Phys 20, 255–281 (1990). https://doi.org/10.1007/BF00731693
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DOI: https://doi.org/10.1007/BF00731693