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.
I am working on extending these bounds to other settings, and testing them in realistic scenarios.
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, 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 (QM) and general relativity (GR) arguments indicate that such perfect clocks are unlikely to exist.
We showed [arXiv 2018] 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.
Measurements have a special role in quantum theory, affecting the subsequent evolution of a state. We have studied the effects that monitoring a quantum system has on its dynamics, and how to exploit measurement back-action for our benefit [PRL 2018].
For monitored many-body systems, the measurement back-action can be thought of as alternate mechanism for the concept of Spontaneous Symmetry Breaking, relevant to a wide range of phenomena. The properties of the symmetry breaking is in such case drastically dependent on the nature of the quantum measurement performed [arXiv 2018].
Moreover, the speed of evolution that one would expect to have changes drastically depending on whether one has access to the measurement outcomes or not [arXiv 2018].
We also studied what happens when one incorporates both anterior and posterior outcomes to determine what occurred to the evolution. One can then 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 [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.