Bell nonlocality and quantum teleportation under noisy channels in high dimensional systems

Abstract

The first part of this thesis is devoted to address the problem of Bell nonlocality quantification. For this, it is introduced a measure of nonlocality associated with a quantum state embedded in a specific measurement context dictated by a Bell inequality. Under this approach the amount of nonlocality is closely related to the ability that a quantum state has to reveal non-classical features when submitted to unbiased local random measurements. It is shown that by employing this figure of merit, the most nonlocal states correspond to the maximally entangled ones for the considered scenarios, especially for the case of pairs of entangled d-level systems under two local measurements per party for which the most known measures of nonlocality do not exhibit such an agreement, (Quant. Inf. Comput. 7, 157, 2008). Another interesting observation is that the amount of nonlocality diminishes with the inverse o the local dimension d of the subsystems, and thus revealing the emergence of classicality in the limit of large quantum numbers. In the second part it is investigated how to improve the performance of several quantum information protocols when noise affects the system. First it is proved that the replacement of EPR states and measurements by their GHZ counterparts may improve the efficiency in the execution of the teleportation and super-dense coding protocols when the qubits may suffer bit-flip noise in the weak regime. Furthermore, it was performed a characterization of the usual protocol of teleportation for qudits for the case in which the involved parts may be affected by some of the most known instances of noise and/or the channel and measurements are not ideal. The idea of fighting noise with noise, presented by Fortes and Rigolin (Phys. Rev. A 92, 012338, 2015), is studied for arbitrary dimension d.