Quantum analogs of classical random walks have been defined in quantum information theory as a useful concept to implement algorithms. Due to interference effects, statistical properties of quantum walks can drastically differ from their classical counterparts, leading to much faster computations.

We shall present various statistical properties of continuous-time quantum walks on a ...

The classical first-passage theory for random walks is generalized to quantum systems by using repeated attempts with a fixed frequency $1/\tau$ to find the system in the detection state $| \psi_\text{d}\rangle$. The first successful of these attempts defines the time $T = N \tau$ of first *detected* arrival. Here, the Zeno limit $\tau\to0$ of diverging detection frequency is investigated. The...

The model of a step quantum heat engine (SQHE) is defined as a working body, given by the two-level system (TLS), acting separately (i.e. in steps) with the heat baths and the energy storage system (a battery). A single step of the engine is defined as the unitary and energy conserving operation. For the general SQHE we prove the fundamental attainable efficiency, given as a function of a cold...