General Upper Bounds on Fluctuations of Trajectory Observables.

Thermodynamic uncertainty relations (TURs) are general lower bounds on the size of fluctuations of dynamical observables. They have important consequences, one being that the precision of estimation of a current is limited by the amount of entropy production. Here, we prove the existence of general upper bounds on the size of fluctuations of any linear combination of fluxes (including all time-integrated currents or dynamical activities) for continuous-time Markov chains.

Towards a Theory of Metastability in Open Quantum Dynamics.

By generalizing concepts from classical stochastic dynamics, we establish the basis for a theory of metastability in Markovian open quantum systems. Partial relaxation into long-lived metastable states-distinct from the asymptotic stationary state-is a manifestation of a separation of time scales due to a splitting in the spectrum of the generator of the dynamics. We show here how to exploit this spectral structure to obtain a low dimensional approximation to the dynamics in terms of motion in a manifold of metastable states constructed from the low-lying eigenmatrices of the generator.

Equivalence of matrix product ensembles of trajectories in open quantum systems.

The equivalence of thermodynamic ensembles is at the heart of statistical mechanics and central to our understanding of equilibrium states of matter. Recently, a formal connection has been established between the dynamics of open quantum systems and statistical mechanics in an extra dimension: an open system dynamics generates a matrix product state (MPS) encoding all possible quantum jump trajectories which allows to construct generating functions akin to partition functions. For dynamics generated by a Lindblad master equation, the corresponding MPS is a so-called continuous MPS which encodes the set of continuous measurement records terminated at some fixed total observation time.

Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state.

We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions.

Asymptotic inference in system identification for the atom maser.

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e.

The elusive Heisenberg limit in quantum-enhanced metrology.

Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes.