Entropy production in the quantum measurement of continuous observables

The von Neumann entropy produced during the quantum measurement of an observable with a continuous spectrum is calculated and shown to depend on the accuracy epsilon of the measurement as D-I In(1/epsilon) where D-I is the so-called information dimension of the probability distribution of the eigenvalues observed if the system is in a given quantum state. Accordingly, the thermodynamic cost is larger for finer accuracy, unless the spectrum is purely discrete, in which case D-I = 0. (c) 2012 Elsevier B.V. All rights reserved.