OPEN QUANTUM SYSTEMS
The realistic description of essentially any physical system should take into account its unavoidable interaction with the surrounding environment, thus treating it as an open system. This is indeed quite a generic statement, which can be applied to both classical and quantum physics, but when it comes to the quantum realm there are (at least) two specific reasons of interest towards the open nature of physical systems. On a practical side, the interaction of a quantum system with its environment strongly influences precisely those features, such as quantum coherence and entanglement, that are distinctively quantum and that are the key resources in a countless number of applications. From a fundamental perspective, any quantum system that is being measured, and that is then coupled to a measurement apparatus, is an instance of a quantum system interacting with a (macroscopic) environment. The theory of open quantum systems is thus naturally linked to the very ground of quantum mechanics, providing us with a bridge between the closed-system unitary evolution and the statistics and state transformations associated with the measurement of the system's observables.
In my research activity, I study how to describe general classes of open quantum system dynamics, focusing both on their mathematical characterization and on the understanding of the physical mechanisms leading to different kinds of evolutions. My investigation addresses different approaches to open quantum systems, as well as their mutual connections; namely, master equations, dynamical maps and perturbative techniques, but also stochastic methods and general strategies to simulate the dynamics of open systems interacting with complex environments via simpler auxiliary models. In addition, I am interested into the explanation of the physical origin of the occurrence of memory effects in open-system dynamics (i.e., non-Markovianity), in terms of both specific features of the evolution and the microscopic characterization of the open system, the environment and their interaction.
My activity is mainly a theoretical one, but I have also been working in strict collaboration with several experimental groups, especially within the context of quantum optical platforms and NV centers in diamonds.
Suggested references: The Theory of Open Quantum Systems, H.-P. Breuer and F. Petruccione, Oxford University Press, 2002
Quantum Noise, C. Gardiner and P. Zoller, Springer, 2004
Open Quantum Systems. An Introduction, Á. Rivas and S.F. Huelga, 2011 -- here the preprint version
QUANTUM METROLOGY
How precisely can we estimate the value of an unknown parameter, once we fix the resources at our disposal? The answer to this question changes dramatically whether we deal with classical or quantum systems and it potentially provides us with a powerful way to exploit quantum features of light and matter to overcome classical standards. As a paradigmatic example, in classical experiments involving N non-interacting sensing particles, the best estimation strategies lead to an error that scales at most as 1/N, according to the shot-noise limit; on the other hand, the use of entangled particles can yield a further factor 1/N of improvement, reaching the so-called Heisenberg limit. Such a quantum advantage is nevertheless jeopardized by the interaction of the sensing systems with the surrounding environment and early results showed that the quantum and classical strategies become equivalent, for example, in the presence of random fluctuations of the parameter to be estimated due to the influence of a fast-decaying environment.
In my research activity, I investigate how and to what extent the limitations to parameter estimation imposed by the presence of noise can be circumvented, thus retaining at least some of the advantage given by the use of quantum systems. The basic idea is to identify the key features of the noise that allow one to access some entanglement among the sensing particles, when proper measurement strategies are devised. This line of research is part of the extremely broad and diversified attempt to formulate a general and fully realistic modeling of the various components involved in different metrological tasks, including the interaction with the environment, but also the preparation and measurement procedures, as well as the possible use of ancillary systems or active interventions on the sensing systems during their evolution.
Suggested references: Advances in Quantum Metrology, V. Giovannetti, S. Lloyd, L. Maccone, Nat. Phot. 5, 222 (2011) -- here the preprint version
Quantum limits in optical interferometry, R. Demkowicz-Dobrzanski, M. Jarzyna, J. Kolodynski, Progress in Optics 60, 345 (2015) -- here the preprint version
FOUNDATIONS OF QUANTUM MECHANICS
More than a century after the birth of quantum mechanics, several questions related to the fundamental meaning of what distinguishes the quantum description of the physical world remain under active investigation. Besides their intrinsic fundamental relevance, these questions are at the basis of the development of upcoming quantum technologies, as well as the understanding of which phenomena are genuinely quantum, for example in biological or thermodynamical systems. In particular, different strategies have been developed to assess the quantumness of physical systems without having to rely on the detailed modeling of the system at hand, but rather directly assessing the probability distributions of the measurement outcomes with respect to specific traits of classical statistics, such as locality, non-contextuality and measurement non-invasiveness.
The starting point of my research activity on this topic is the very defining property of classical stochastic processes, that is, the validity of the so-called Kolmogorov consistency conditions. In fact, the latter allow us to formulate fully operational criteria to evaluate the possible non-classicality of the statistics associated with sequential measurements at different times and to detect when and to what extent specific features of quantum mechanics, such as quantum coherence and non-classical correlations, are actually unambiguously linked to the departure from any classical description of the statistics. A crucial role here is played by the type of measurements that are performed at different times, as well as by the underlying physical process that determines the evolution of the system in between the measurements, especially whether it is able to ``drive forward" the memory about the past measurement outcomes and system transformations. The precise connection of these features with the different facets of memory effects in the classical and quantum realms, for example as fixed by the Hamiltonian description of the system at hand, remains at the moment a multilayered and far from trivial open problem.
Suggested references: Speakable and Unspeakable in Quantum Mechanics, J.S. Bell, Cambridge University Press, 1987
Leggett-Garg Inequalities, C. Emary, N. Lambert, F. Nori, Rep. Prog. Phys. 77, 016001 (2014) -- here the preprint version