Dynamical model selection near the quantum-classical boundary

We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in postselection as well as for real-time analysis, and offers an alternative to statistical tests based on state-reconstruction methods. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using an experiment in levitated optomechanical systems as an example.

Figure 1

Numerically calculated probabilities for the identification of the correct dynamical evolution of an optomechanical example with trapped nanoparticles in a double-well potential: $Q$ is calculated using a quantum stochastic master equation, and $C$ is calculated using the equivalent classical stochastic differential equation. Probabilities $p\left(C\right|C)$ and $p\left(Q\right|Q)$ are shown, for different temperatures $T$ as a function of the measurement efficiency $\eta$. Insets show approximate regions where the models are distinguishable [green (light-gray) shaded regions], as functions of temperature and measurement efficiency.