[en] We propose a definition for the Polya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, the higher-dimensional integer lattices, and a number of other graphs, and we calculate their Polya number. For the timing of the measurements, a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.

[en] We propose a scheme for preparing optical Schroedinger-cat states in a traveling wave setting. Two states are similarly prepared via the self-Kerr effect, and after mixing them, one mode is measured by homodyne detection. In the other mode, a superposition of coherent states is conditionally prepared. The advantage of the scheme is that assuming a small Kerr effect, one can prepare with a high probability one of a set of Schroedinger-cat states. The measured value of the quadrature provides information about which one of the set of states is actually prepared.

[en] Given a source of two coherent state superpositions with small separation in a travelling wave optical setting, we show that by interference and balanced homodyne measurement it is possible to conditionally prepare a symmetrically placed superposition of coherent states around the origin of the phase space. The separation of coherent states in the superposition will be amplified during the process.