We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show that the diffusion coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. When links between neighboring sites are randomly broken with probability p per unit time, the evolution becomes decoherent after a characteristic time that scales as 1/p. The fact that the quadratic increase of the variance is eventually lost even for very small frequencies of disrupting events, suggests that the implementation of a quantum walk on a real physical system may be severely limited by thermal noise and lattice imperfections.

We analyze in detail the discrete-time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.

We show that for two initially excited qubits, interacting via dipole forces and with a common reservoir, entanglement is preceded by the emergence of quantum and classical correlations. After a time lag, entanglement finally starts building up, giving rise to a peculiar entangled state, with very small classical correlations. Different measures of quantum correlations are discussed, and their dynamics are compared and shown to lead to coincident values of these quantifiers for several ranges of time.

We consider a new model of quantum walk on a one dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known quantum kicked rotor, this model can be mapped into a localized one-dimensional Anderson model. For exceptional (rational) values of its scale parameter, the system exhibits resonant behavior and reduces to the usual discrete time quantum walk on the line.

We propose an all-optical setup, which couples different degrees of freedom of a single photon, to investigate entanglement generation by a common environment. The two qubits are represented by the photon polarization and Hermite-Gauss transverse modes, while the environment corresponds to the photon path. For an initially two-qubit separable state, the increase of entanglement is analyzed, as the probability of an environment-induced transition ranges from zero to one. An entanglement witness that is invariant throughout the evolution of the system yields a direct measurement of the concurrence of the two-qubit state.Comment: 11 pages, 3 figure

We study the resonances of the quantum kicked rotor subjected to an excitation that follows an aperiodic Fibonacci prescription. In such a case the secondary resonances show a sub-ballistic behavior like the quantum walk with the same aperiodic prescription for the coin. The principal resonances maintain the well-known ballistic behavior.

We have designed and tested an atomic vectorial magnetometer based on the analysis of the coherent oscillatory transients in the transmission of resonant laser light through a Rb vapor cell. We show that the oscillation amplitudes at the Larmor frequency and its first harmonic are related through a simple formula to the angles determining the orientation of the magnetic field vector. The magnetometer was successfully applied to the measurement of the ambient magnetic field.

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