0000000000324722
AUTHOR
Mari Carmen Bañuls
A study of Wigner functions for discrete-time quantum walks
We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.
Reply to Comment on ‘Wigner function for a particle in an infinite lattice’
In a recent paper (2012 New J. Phys. 14 103009), we proposed a definition of the Wigner function for a particle on an infinite lattice. Here we argue that the criticism to our work raised by Bizarro is not substantial and does not invalidate our proposal.
Non-Markovianity and memory of the initial state
We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the BLP measure proposed in \cite{breuer2009}. We illustrate our findings with explicit calculations for the case of a structured environment.