The unavoidable interaction of a quantum system with its environment usually degrades its coherence and quantumness. The environment and the decoherence process may be described as the interaction with a classical or quantized bath. As a matter of fact, the classical description becomes progressively more reliable as far as the environment has many degrees of freedom, i.e. it becomes complex, or when the interaction between a quantum system and a classical fluctuating field is taken into account. In this thesis, I consider a qubit system coupled to a stochastic classical field and address�the decoherence and non-Markovianity induced by the external noise as well as the spectral characterization of the classical field by quantum-limited measurement on the qubit. I thus analyze the dynamics of quantum correlations between two non-interacting, initially entangled qubits subject to a classical noise generated by a stochastic process. Two relevant classes of noise are taken into account: Gaussian noise, such as the Ornstein-Uhlenbeck process, and non-Gaussian noise, such as the random telgraph noise and the colored noise with 1/f spectrum. I also discuss the evaluation of non-Markovianity of the induced dynamical map and link the presence of revivals of quantum correlations with the information backflow to the system. The precise characterization of the stochastic process generating the classical noise, possibly using minimal resources, is a crucial ingredient for the design of high-precision measurements and reliable communication protocols. To this purpose, I also address the characterization of the spectral parameters of classical noise by quantum probes, e.g. a qubit coupled to the stochastic process generating the noise. By using the tools of quantum estimation theory, I explore the performances of quantum measurements on the qubit and show that it is possible to effectively extract information about the noise.
Entanglement has been proposed as a means to improve the sensitivity of sensing weak signals. While the degree of this quantum advantage is well understood in noiseless settings, the situation is more complex under realistic conditions, where the system is subject to decoherence. In this case, the enhancement depends on the specific noise characteristics. Previous treatments of colored noise typically assume that the noise is uncorrelated between successive experiments. Here, we consider the scenario in which the noise exhibits correlations across multiple shots. We derive a simple fundamental limit to the sensitivity based on the fact that the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. Focusing on Ramsey spectroscopy with probes affected by pure classical dephasing, we show that, for suitable spatial and temporal noise correlations, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This demonstrates that entanglement can provide a substantial improvement for Ramsey spectroscopy subject to correlated noise.
As demand for quantum technologies increases, so does the need to generate and classify non-classical correlations in complex many-body systems. We introduce a simple and versatile method for creating and certifying entanglement and many-body Bell correlations. This method relies on a single qubit interacting with an
N-qubit system. We demonstrate that: (i) such pairwise interaction is sufficient to induce many-body quantum correlations, and (ii) the qubit can serve as a probe to extract all information about these correlations. Thus, single-qubit measurements reveal multi-partite entanglement and
N-body Bell correlations, enabling the rapid and efficient certification of non-classicality in complex systems.