Dissipative quantum systems: theoretical foundations and applications

Motivated by the continuous advancements in the miniaturization of devices down to reveal the quantum nature of matter, in this thesis we investigate the way a quantum system is affected by the presence of a thermal environment and propose methodologies to exploit this kind of sensitivity for quantum technologies. Since treating exactly the dynamics of the full system-environment compound is generally problematic for the diverging number of degrees of freedom involved in the calculation, effective master equations for the reduced system density matrix were developed in literature during the last century. Among them, the Redfield approach is an equation obtained under weakcoupling (or Born) and Markovian assumptions. Despite offering effective descriptions in a plethora of situations, it was criticized for not preserving the positivity (and hence the complete positivity) of the system density matrix. The latter property is in general a fundamental feature for assigning a probabilistic interpretation to the theory. We hence begin by facing the problem of the non-positivity character of the Redfield equation, curing it of the strict amount that is necessary via coarse-grain averaging performed on the Redfield equation in the interaction picture. In the analysis a central role is played by the coarse grain timescale. Once set it equal to a critical threshold value, the resulting equation (CP-Redfield) enables conserving the predictive power of the Redfield approach and preserving positivity at the same time. About it, we report both practical estimation and self-consistent methods to evaluate the critical timescale. Our strategy also allows to continuously map the Redfield equation into the secular master equation (diverging coarse-grain time interval) by appropriately tuning the coarse grain time, the latter being the equation usually adopted in the literature for ensuring thermodynamic consistency by enforcing a rotating-wave approximation. Starting from a minimal example concerning the dipole coupling between a qubit and a bosonic bath, we then apply this methodology to dissipative multipartite systems, for which the local vs global debate is of current interest. The local master equation is instead the equation that is obtained by assigning to each subsystem its proper thermal dissipator, preserving the local character of the microscopic interactions, while the global approach is the Redfield equation in the secular limit. In this context, we studied an asymmetric energy transfer model constituted by harmonic oscillators which, being exactly solvable, provides the appropriate benchmark for testing the efficiency of the different master equations.. Beyond finding useful the application of the CP-Redfield equation, we point out a sensible convex-mixture of the local and global solutions based on the timescale separation of the two strategies. The local approach is then applied in the context of quantum batteries, a field that was previously analyzed under closed (i.e. Hamiltonian) settings. We hence provide one of the first attempts of schematizing an open quantum battery, where, recalling in part the aforementioned asymmetric model, the charging process originates from external sources (coherent and/or noisy) and is mediated by a proper quantum charger. By studying different implementations, particular attention was devoted to find possible interplay between coherent and incoherent energy supply mechanisms in producing stored energy and ergotropy, the latter being defined in literature as the maximum extractable work. As a central result, increasing temperature is not always detrimental for the stored ergotropy. Going beyond the particular instance of bosonic bath, the sensitivity of a quantum system to its surrounding environment is finally exploited in the context of statistical tagging, where one aims to guess the quantum statistics (fermionic or bosonic) of a thermal bath of interest, introducing in this way a novel research line in the field of quantum metrology. We propose an indirect measurement protocol in which a quantum probe is let to interact with the unknown bath and relies on the consideration that, despite the final probe equilibrium configuration is not necessarily influenced by the bath nature, the latter generally leaves residual imprintings in the probe state before thermalization, i.e. out-of-equilibrium. Using figures of merit taken from quantum metrology such as the Holevo-Helstrom probability of error and the quantum Chernoff bound, we treated the cases of qubit and harmonic oscillator probes, finding that, generally, the presence of coherences in the input state of the probe is beneficial for the discrimination capability and noticing a bosonic advantage in reducing to zero the error probability.