Thermodynamics of N-dimensional quantum walks

The entanglement between the position and coin state of a $N$-dimensional quantum walker is shown to lead to a thermodynamic theory. The entropy, in this thermodynamics, is associated to the reduced density operator for the evolution of chirality, taking a partial trace over positions. From the asymptotic reduced density matrix it is possible to define thermodynamic quantities, such as the asymptotic entanglement entropy, temperature, Helmholz free energy, etc. We study in detail the case of a $2$-dimensional quantum walk, in the case of two different initial conditions: a non-separable coin-position initial state, and a separable one. The resulting entanglement temperature is presented as function of the parameters of the system and those of the initial conditions.Comment: 10 pages, 4 fig

Preserving Privacy in a Smart Grid Scenario using Quantum Mechanics

Studies on smart grid and quantum mechanics have potential to yield several benefits to society, with the former resulting in economic and environmental benefits and the latter providing perfect security and privacy at affordable costs. Recently, security and privacy have become important issues in electrical power grids. In this paper, we describe two quantum privacy-enhancing protocols: one of them requires that the parties initially share a certain amount of quantum entangled states, while the other uses only quantum key distribution methods without sharing quantum entangled states. The two proposed protocols are resistant to attacks from quantum computers. This paper also describes some recent advances of classical and quantum privacy-enhancing technologies