QUANTUM PROBING AND CHARACTERIZATION TECHNIQUES FOR SYSTEMS OF INTEREST IN QUANTUM INFORMATION PROCESSING.

The thread of this thesis is an attempt to clarify some assumptions that sound reasonable but whose correctness has never been proved or demonstrated formally. The first question I consider is: Do two quantum states near in the Hilbert space have the same, or almost the same, physical properties? First of all we have to clarify with which kind of measure we would like to measure the distance between two states. I do consider a measure, called Fidelity, that acts from the Hilbert space of a bipartite system to [0; 1]. Fidelity is null when the two states are orthogonal while if it is 1 the two states coincides. I show that high fidelities may be achieved by pairs of states with considerably different physical properties, including separable and entangled states or classical and nonclassical ones. Therefore, fidelity alone cannot be used to asses the very quantum properties of two states,but a tomographic reconstruction of the state is required. Secondly I question: Does a good quantum thermometer could be build with a system showing phase transition? I employ a critical magnetic system, known as Lipkin-Meshkov-Glick model, I study it in contact with a reservoir with it has thermalized but whose temperature is an unknown temperature to be estimated. I show that the best precision for temperature estimation it is not at critical point as someone could suspect but nevertheless criticality is an unmatchable resource even in the quantum realm. Last question is: when two different probes spatially separated interact with a common or a separate bath? It is quite a common opinion that systems, two objects located far away one from each others, feel the effect of different environments. Dissipation and decoherence are the two main processes which a quantum system undergo when it is not isolated, but when it interacts with another system much bigger. I explore how two different systems put in contact with a common bath show decoherence with typical quantum interference leading to a non obvious definition of separate environments.