Classical robustness of quantum unravellings

– We introduce three measures which quantify the degree to which quantum systems possess the robustness exhibited by classical systems when subjected to continuous observation. Using these we show that for a fixed environmental interaction the level of robustness depends on the measurement strategy, or unravelling, and that no single strategy is maximally robust in all ways. When describing the observation of individual quantum systems, it is crucial to explicitly treat the measurement process using quantum measurement theory. The reverse, however, is commonly true for classical systems —it is quite usual for experimentalists both to model and gather data about classical systems without any reference to classical measurement theory (being the theory of Bayesian statistical inference or nonlinear filtering [1,2]). This dramatic contrast is only possible because of certain properties which many classical systems possess. Three such properties are apparent if we consider watching the motion of a pendulum: 1) when we open our eyes, we obtain the information (the location and velocity of the pendulum) almost instantaneously; 2) the information we obtain is not exclusive —many people can observe the same system, and will all agree upon the results; and 3) the system is relatively unaffected by noise so that if we close our eyes for a moment, we can accurately predict what we will see when we open them again(). We will refer to the degree to which a system possesses these properties as its degree of robustness under each property. The classical robustness of quantum systems in this sense was the subject of a recent study by Dalvit, Dziamarga and Zurek [3]. They concluded that, for a given environmental interaction, a single measurement strategy will maximize the robustness for both properties 1) and 3) above. Here we investigate the degree of robustness of two canonical quantum systems for the three properties above (and a fourth), under a wide class of measurement strategies. We show that this conclusion is, in fact, not warranted. That is, in general, for a fixed environmental interaction, different measurement strategies are required to maximize (1)Note that the existence of chaos in a system does not destroy its robustness: in this case, the divergence of neighboring trajectories is exponential and thus has a negligible effect on the predictability for short times.