Advances in quantum technologies, which determine the success of the second quantum revolution, represent an important goal of modern science. Quantum information processing and communication protocols and tasks like quantum computing, quantum teleportation and quantum cryptography are based on the quantum information theory.

In the first part of the thesis we describe the temporal evolution of quantum fidelity for an initial Gaussian squeezed state of a two-mode bosonic system placed in a thermal environment. Then, we apply the fidelity concept to the quantum teleportation protocol, and evaluate the fidelity of teleportation of a coherent state using an entangled two-mode Gaussian state as a resource. We analyze the dependence in time of the fidelity of teleportation on the squeezing parameter, coupling between modes and temperature of the bath. In addition, we calculate the logarithmic negativity, which measures the strength of the entanglement, in order to confirm the possibility of a successful teleportation.

In the second part of the thesis we describe a novel phenomenon, that takes place in highly dissipative arrays of Josephson junctions, which appear in high temperature superconductors placed in near-critical conditions. In the studied arrays, besides the Stewart-McCumber hysteresis a “collective hysteresis” associated with generation of charge traveling waves appears for the overcritical currents. This phenomenon could be used in implementation of high temperature superconducting qubits.

In the last part of the thesis we suggest that graphene coating can significantly improve ion traps performance, and propose an arc discharge method for multilayer graphene synthesis. Other materials obtained during the synthesis process could find their place in different applications. In particular, we propose to use amorphous carbon for improving the solar air heaters performance.