215 research outputs found
Dynamical Localization in Quasi-Periodic Driven Systems
We investigate how the time dependence of the Hamiltonian determines the
occurrence of Dynamical Localization (DL) in driven quantum systems with two
incommensurate frequencies. If both frequencies are associated to impulsive
terms, DL is permanently destroyed. In this case, we show that the evolution is
similar to a decoherent case. On the other hand, if both frequencies are
associated to smooth driving functions, DL persists although on a time scale
longer than in the periodic case. When the driving function consists of a
series of pulses of duration , we show that the localization time
increases as as the impulsive limit, , is
approached. In the intermediate case, in which only one of the frequencies is
associated to an impulsive term in the Hamiltonian, a transition from a
localized to a delocalized dynamics takes place at a certain critical value of
the strength parameter. We provide an estimate for this critical value, based
on analytical considerations. We show how, in all cases, the frequency spectrum
of the dynamical response can be used to understand the global features of the
motion. All results are numerically checked.Comment: 7 pages, 5 figures included. In this version is that Subsection III.B
and Appendix A on the quasiperiodic Fermi Accelerator has been replaced by a
reference to published wor
Quantum walk as a generalized measuring device
We show that a one-dimensional discrete time quantum walk can be used to
implement a generalized measurement in terms of positive operator value measure
(POVM) on a single qubit. More precisely, we show that for a single qubit any
set of rank 1 and rank 2 POVM elements can be generated by a properly
engineered quantum walk. In such a scenario the measurement of particle at
position x=i corresponds to a measurement of a POVM element E_i on a qubit. We
explicitly construct quantum walks implementing unambiguous state
discrimination and SIC-POVM.Comment: 6 pages, 1 figur
Spatial search in a honeycomb network
The spatial search problem consists in minimizing the number of steps
required to find a given site in a network, under the restriction that only
oracle queries or translations to neighboring sites are allowed. In this paper,
a quantum algorithm for the spatial search problem on a honeycomb lattice with
sites and torus-like boundary conditions. The search algorithm is based on
a modified quantum walk on a hexagonal lattice and the general framework
proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity
of this quantum search algorithm is .Comment: 10 pages, 2 figures; Minor typos corrected, one Reference added.
accepted in Math. Structures in Computer Science, special volume on Quantum
Computin
Spatial quantum search in a triangular network
The spatial search problem consists in minimizing the number of steps
required to find a given site in a network, under the restriction that only
oracle queries or translations to neighboring sites are allowed. We propose a
quantum algorithm for the spatial search problem on a triangular lattice with N
sites and torus-like boundary conditions. The proposed algortithm is a special
case of the general framework for abstract search proposed by Ambainis, Kempe
and Rivosh [AKR05] (AKR) and Tulsi [Tulsi08], applied to a triangular network.
The AKR-Tulsi formalism was employed to show that the time complexity of the
quantum search on the triangular lattice is O(sqrt(N logN)).Comment: 10 pages, 4 Postscript figures, uses sbc-template.sty, appeared in
Annals of WECIQ 2010, III Workshop of Quantum Computation and Quantum
Informatio
Quantum walk on the line: entanglement and non-local initial conditions
The conditional shift in the evolution operator of a quantum walk generates
entanglement between the coin and position degrees of freedom. This
entanglement can be quantified by the von Neumann entropy of the reduced
density operator (entropy of entanglement). In the long time limit, it
converges to a well defined value which depends on the initial state. Exact
expressions for the asymptotic (long-time) entanglement are obtained for (i)
localized initial conditions and (ii) initial conditions in the position
subspace spanned by the +1 and -1 position eigenstates.Comment: A few mistakes where corrected. One of them leads to a factor of 2 in
eq. (49), the other results remain unchanged. In this version, several
figures where replaced by color version
Conditional Quantum Walk and Iterated Quantum Games
Iterated bipartite quantum games are implemented in terms of the
discrete-time quantum walk on the line. Our proposal allows for conditional
strategies, as two rational agents make a choice from a restricted set of
two-qubit unitary operations. Several frequently used classical strategies give
rise to families of corresponding quantum strategies. A quantum version of the
Prisoner's Dilemma in which both players use mixed strategies is presented as a
specific example. Since there are now quantum walk physical implementations at
a proof-of principle stage, this connection may represent a step towards the
experimental realization of quantum games.Comment: Revtex 4, 6 pages, 3 figures. Expanded version with one more figure
and updated references. Abstract was rewritte
Quantum random walk on the line as a markovian process
We analyze in detail the discrete--time quantum walk on the line by
separating the quantum evolution equation into Markovian and interference
terms. As a result of this separation, it is possible to show analytically that
the quadratic increase in the variance of the quantum walker's position with
time is a direct consequence of the coherence of the quantum evolution. If the
evolution is decoherent, as in the classical case, the variance is shown to
increase linearly with time, as expected. Furthermore we show that this system
has an evolution operator analogous to that of a resonant quantum kicked rotor.
As this rotator may be described through a quantum computational algorithm, one
may employ this algorithm to describe the time evolution of the quantum walker.Comment: few typos corrected, 13 pages, 2 figures, to appear in Physica
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