Quantum correlations in information theory - Girolami, Davide (2013)
The project concerned the study of quantum correlations (QC) in compound systems, i.e. statistical correlations more general than entanglement which are predicted by quantum mechanics but not described in any classical scenario. I aimed to understand the technical and operational properties of the measures of QC, their interplay with entanglement quantifiers and the experimental accessibility. In the first part of my research path, after having acquired the conceptual and technical rudiments of the project, I provided solutions for some computational issues: I developed analytical and numerical algorithms for calculating bipartite QC in finite dimensional systems. Then, I tackled the problem of the experimental detection of QC. There is no Hermitian operator associated with entanglement measures, nor with QC ones. However, the information encoded in a density matrix is redundant to quantify them, thus the full knowledge of the state is not required to accomplish the task. I reported the first protocol to measure the QC of an unknown state by means of a limited number of measurements, without performing the tomography of the state. My proposal has been implemented experimentally in a NMR (Nuclear Magnetic Resonance) setting. In the final stage of the project, I explored the foundational and operational merits of QC. I showed that the QC shared by two subsystems yield a genuinely quantum kind of uncertainty on single local observables. The result is a promising evidence of the potential exploitability of separable (unentangled) states for quantum metrology in noisy conditions.