Entropy production in the quantum measurement of continuous observables

► Von Neumann has shown that entropy is produced during quantum measurements. ► This entropy depends on the spectrum of the measured observable. ► For a continuous spectrum, the entropy increases with the accuracy of the measurement. ► The finer the accuracy, the larger the thermodynamic cost. ► In general, the entropy is proportional to the information dimension of the spectrum and the logarithm of the accuracy.