Previous work showed that closed quantum systems equilibrate under very general conditions, but gave no estimates for the timescales of such process. During my PhD we found that, without further restrictions, there always exist observables that equilibrate in extremely long times (longer than the age of the universe even for quite small systems!) [PRE 2014].
This provided an important lesson: it is essential to restrict to physically meaningful observables in order to prove reasonably fast equilibration.
We also achieved significant advances in this direction: we found conditions on the observable, initial state, and Hamiltonian trio which ensure improved upper bounds on the equilibration time scales [PRX 2017]. These bounds are tight, and significantly simpler to calculate than solving the exact dynamics of the system.
A sequence of past outcomes from measurements performed on a quantum system can be used to learn about its evolution. Perhaps unsurprisingly, this measurement output is fully characterized by the state of the system: the best tool we have to predict results of measurements in quantum theory.
However, if one incorporates both anterior and posterior outcomes one can construct smoothed estimates of a measured observable that characterize the measurement output at a given time better than any quantity derived from full knowledge of the instantaneous state of the system [our paper on this was chosen as an Editors’ Suggestion on PRA].
This shifts the status of the quantum state of a system: while it remains the best tool to predict, it is not the most appropriate tool to describe past dynamics.
In general, quantum states cannot be interpreted as classical probability distributions. In particular, given a coherent superposition of two states, one cannot think of the system as being in either of those states, with a certain probability for each. In unitary quantum mechanics these superposition states always remain as such, a fact that is at the root of the difficulty in defining the occurrence of quantum events.
However, people have pointed out that it is only with access to an ideal clock that one would be able to perceive the underlying unitary evolution of a quantum system in an experiment. A combination of quantum mechanical and general relativity arguments indicate that such perfect clocks are unlikely to exist.
We showed that if fundamental time uncertainties exist, then situations naturally arise in which no measurement allows to verify that a system is in a quantum superposition. That is, from the point of view of physically observable predictions, in such situations the system behaves exactly as if it were in a classically interpretable state. We built on this idea to develop the Montevideo Interpretation of Quantum Mechanics, a realist view of how events and measurements happen in a quantum world.