326 research outputs found
Crossovers induced by discrete-time quantum walks
We consider crossovers with respect to the weak convergence theorems from a
discrete-time quantum walk (DTQW). We show that a continuous-time quantum walk
(CTQW) and discrete- and continuous-time random walks can be expressed as DTQWs
in some limit. At first we generalize our previous study [Phys. Rev. A
\textbf{81}, 062129 (2010)] on the DTQW with position measurements. We show
that the position measurements per each step with probability can be evaluated, where is the final time and . We
also give a corresponding continuous-time case. As a consequence, crossovers
from the diffusive spreading (random walk) to the ballistic spreading (quantum
walk) can be seen as the parameter shifts from 0 to 1 in both discrete-
and continuous-time cases of the weak convergence theorems. Secondly, we
introduce a new class of the DTQW, in which the absolute value of the diagonal
parts of the quantum coin is proportional to a power of the inverse of the
final time . This is called a final-time-dependent DTQW (FTD-DTQW). The CTQW
is obtained in a limit of the FTD-DTQW. We also obtain the weak convergence
theorem for the FTD-DTQW which shows a variety of spreading properties.
Finally, we consider the FTD-DTQW with periodic position measurements. This
weak convergence theorem gives a phase diagram which maps sufficiently
long-time behaviors of the discrete- and continuous-time quantum and random
walks.Comment: 14 pages, 1 figur
Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord
Noisy quantum walks are studied from the perspective of comparing their
quantumness as defined by two popular measures, measurement-induced disturbance
(MID) and quantum discord (QD). While the former has an operational definition,
unlike the latter, it also tends to overestimate non-classicality because of a
lack of optimization over local measurements. Applied to quantum walks, we find
that MID, while acting as a loose upper bound on QD, still tends to reflect
correctly the trends in the behavior of the latter. However, there are regimes
where its behavior is not indicative of non-classicality: in particular, we
find an instance where MID increases with the application of noise, where we
expect a reduction of quantumness.Comment: 5 pages with 4 figures, Published Versio
Robustness of topologically protected edge states in quantum walk experiments with neutral atoms
Discrete-time quantum walks allow Floquet topological insulator materials to
be explored using controllable systems such as ultracold atoms in optical
lattices. By numerical simulations, we study the robustness of topologically
protected edge states in the presence of decoherence in one- and
two-dimensional discrete-time quantum walks. We also develop a simple
analytical model quantifying the robustness of these edge states against either
spin or spatial dephasing, predicting an exponential decay of the population of
topologically protected edge states. Moreover, we present an experimental
proposal based on neutral atoms in spin-dependent optical lattices to realize
spatial boundaries between distinct topological phases. Our proposal relies on
a new scheme to implement spin-dependent discrete shift operations in a
two-dimensional optical lattice. We analyze under realistic decoherence
conditions the experimental feasibility of observing unidirectional,
dissipationless transport of matter waves along boundaries separating distinct
topological domains.Comment: 16 pages, 10 figure
Limit theorems for the interference terms of discrete-time quantum walks on the line
The probability distributions of discrete-time quantum walks have been often
investigated, and many interesting properties of them have been discovered. The
probability that the walker can be find at a position is defined by diagonal
elements of the density matrix. On the other hand, although off-diagonal parts
of the density matrices have an important role to quantify quantumness, they
have not received attention in quantum walks. We focus on the off-diagonal
parts of the density matrices for discrete-time quantum walks on the line and
derive limit theorems for them.Comment: Quantum Information and Computation, Vol.13 No.7&8, pp.661-671 (2013
- …