We build on the seminal work by Brun, Carteret and Ambainis to reconsider dissipative quantum walks, induced by noisy coin operations. Motivated by the prospect of performing coin-operation tomography on the basis of positional data, we develop a comprehensive framework for calculating positional data analytically for time-discrete quantum walks on a 1D-lattice under noisy coin operations. To that end, we transform the dynamics into Fourier space and focus on the weak-noise, long-time limit.
In this talk I will show that there is more to find than the naively expected quantum-to-classical crossover with ultimately Gaussian probability densities in position space, and I will try to explain some of the mathematical subtleties involved in the analytical calculation.