Simultaneous measurements

The dynamic description of simultaneous measurements of conjugate observables (e. g., position and momentum) dates back to the theory of Arthurs and Kelly. In their pioneering work, they considered a model of two pointer systems, which are coupled to a quantum system to be measured and act as the measurement apparatus. Many questions for further research unfold from this original approach. Particularly interesting is the quest for an accurate measurement with the least possible uncertainty. Another important aspect is the study of decoherence effects as a possible explanation for the transition from quantum mechanics to classical mechanics during the measurement process.

We extend the original model of Arthurs and Kelly by (i) using time-dependent interactions, and (ii) including a thermal environment in which the pointers behave as coupled particles under Brownian motion. This novel approach leads us to so-called open pointer-based simultaneous measurements of conjugate observables. Using variances and information entropy we determine the measurement accuracy and find a new kind of entropic uncertainty relation which is an improvement of a previous result [5]. We are also able to show the emergence of decoherence effects as a consequence of the coupling to the environment.