1,595 research outputs found
Study of continuous-time quantum walks on quotient graphs via quantum probability theory
In the present paper, we study the continuous-time quantum walk on quotient
graphs. On such graphs, there is a straightforward reduction of problem to a
subspace that can be considerably smaller than the original one. Along the
lines of reductions, by using the idea of calculation of the probability
amplitudes for continuous-time quantum walk in terms of the spectral
distribution associated with the adjacency matrix of graphs [Jafarizadeh and
Salimi (Ann. Phys 322(2007))], we show the continuous-time quantum walk on
original graph induces a continuous-time quantum walk on quotient
graph . Finally, for example we investigate continuous-time quantum
walk on some quotient Cayley graphs.Comment: 18 pages, 4 figure
Non-Markovianity by Quantum Loss
In the study of open quantum systems, information exchange between system and
its surrounding environment plays an eminent and important role in analysing
the dynamics of open quantum system. In this work, by making use of the quantum
information theory and intrinsic properties such as \emph{entropy exchange},
\emph{coherent information} and using the notion of \emph{quantum loss} as a
criterion of the amount of lost information, we will propose a new witness,
based on information exchange, to detect non-Markovianity. Also a measure for
determining the degree of non-Markovianity, will be introduced by using our
witness. The characteristic of non-Markovianity is clarified by means of our
witness, and we emphasize that this measure is constructed based on the loss of
information or in other word the rate of \emph{quantum loss} in the
environment. It is defined in term of reducing correlation between system and
ancillary. Actually, our focus is on the information which be existed in the
environment and it has been entered to the environment due to its interaction
with the system. Remarkably, due to choosing the situation which the "system
+ancillary" in maximal entangled pure state, optimization procedure does not
need in calculation of our measure, such that the degree of non-Markovianity is
computed analytically by straightforward calculations.Comment: 6 pages, 2 figure
Mixing-time and large-decoherence in continuous-time quantum walks on one-dimension regular networks
In this paper, we study mixing and large decoherence in continuous-time
quantum walks on one dimensional regular networks, which are constructed by
connecting each node to its nearest neighbors( on either side). In our
investigation, the nodes of network are represented by a set of identical
tunnel-coupled quantum dots in which decoherence is induced by continuous
monitoring of each quantum dot with nearby point contact detector. To formulate
the decoherent CTQWs, we use Gurvitz model and then calculate probability
distribution and the bounds of instantaneous and average mixing times. We show
that the mixing times are linearly proportional to the decoherence rate.
Moreover, adding links to cycle network, in appearance of large decoherence,
decreases the mixing times.Comment: 21 pages, 2 figures, accepted for publication in Quantum Information
Processin
Tightening the entropic uncertainty bound in the presence of quantum memory
The uncertainty principle is a fundamental principle in quantum physics. It
implies that the measurement outcomes of two incompatible observables can not
be predicted simultaneously. In quantum information theory, this principle can
be expressed in terms of entropic measures. Berta \emph{et al}.
[\href{http://www.nature.com/doifinder/10.1038/nphys1734}{ Nature Phys. 6, 659
(2010) }] have indicated that uncertainty bound can be altered by considering a
particle as a quantum memory correlating with the primary particle. In this
article, we obtain a lower bound for entropic uncertainty in the presence of a
quantum memory by adding an additional term depending on Holevo quantity and
mutual information. We conclude that our lower bound will be tighten with
respect to that of Berta \emph{et al.}, when the accessible information about
measurements outcomes is less than the mutual information of the joint state.
Some examples have been investigated for which our lower bound is tighter than
the Berta's \emph{et al.} lower bound. Using our lower bound, a lower bound for
the entanglement of formation of bipartite quantum states has obtained, as well
as an upper bound for the regularized distillable common randomness.Comment: 6 pages, 1 figure to appear in PRA 201
Perfect state transfer via quantum probability theory
The transfer of quantum states has played an important role in quantum
information processing. In fact, transfer of quantum states from point to
with unit fidelity is very important for us and we focus on this case. In
recent years, in represented works, they designed Hamiltonian in a way that a
mirror symmetry creates with with respect to network center. In this paper, we
stratify the spin network with respect to an arbitrary vertex of the spin
network o then we design coupling coefficient in a way to create a mirror
symmetry in Hamiltonian with respect to center. By using this Hamiltonian and
represented approach, initial state that have been encoded on the first vertex
in suitable time and with unit fidelity from it's antipodes vertex can be
received. In his work, there is no need to external control.Comment: 23 pag
Investigation of Continuous-Time Quantum Walk Via Spectral Distribution Associated with Adjacency Matrix
Using the spectral distribution associated with the adjacency matrix of
graphs, we introduce a new method of calculation of amplitudes of
continuous-time quantum walk on some rather important graphs, such as line,
cycle graph , complete graph , graph , finite path and some
other finite and infinite graphs, where all are connected with orthogonal
polynomials such as Hermite, Laguerre, Tchebichef and some other orthogonal
polynomials. It is shown that using the spectral distribution, one can obtain
the infinite time asymptotic behavior of amplitudes simply by using the method
of stationary phase approximation(WKB approximation), where as an example, the
method is applied to star, two-dimensional comb lattices, infinite Hermite and
Laguerre graphs. Also by using the Gauss quadrature formula one can approximate
infinite graphs with finite ones and vice versa, in order to derive large time
asymptotic behavior by WKB method. Likewise, using this method, some new graphs
are introduced, where their amplitude are proportional to product of amplitudes
of some elementary graphs, even though the graphs themselves are not the same
as Cartesian product of their elementary graphs. Finally, via calculating mean
end to end distance of some infinite graphs at large enough times, it is shown
that continuous time quantum walk at different infinite graphs belong to
different universality classes which are also different than those of the
corresponding classical ones.Comment: 38 pages, 3 figures, regular pape
The role of the total entropy production in dynamics of open quantum systems in detection of non-Markovianity
In the theory of open quantum systems interaction is a fundamental concepts
in the review of the dynamics of open quantum systems. Correlation, both
classical and quantum one, is generated due to interaction between system and
environment. Here, we recall the quantity which well known as total entropy
production. Appearance of total entropy production is due to the entanglement
production between system an environment. In this work, we discuss about the
role of the total entropy production for detecting non-Markovianity. By
utilizing the relation between total entropy production and total correlation
between subsystems, one can see a temporary decrease of total entropy
production is a signature of non-Markovianity.Comment: 5 pages and 4 figure
Investigation of Continuous-Time Quantum Walk Via Modules of Bose-Mesner and Terwilliger Algebras
The continuous-time quantum walk on the underlying graphs of association
schemes have been studied, via the algebraic combinatorics structures of
association schemes, namely semi-simple modules of their Bose-Mesner and
(reference state dependent) Terwilliger algebras. By choosing the (walk)
starting site as a reference state, the Terwilliger algebra connected with this
choice turns the graph into the metric space, hence stratifies the graph into a
(d+1) disjoint union of strata, where the amplitudes of observing the
continuous-time quantum walk on all sites belonging to a given stratum are the
same. In graphs of association schemes with known spectrum, the transition
amplitudes and average probabilities are given in terms of dual eigenvalues of
association schemes. As most of association schemes arise from finite groups,
hence the continuous-time walk on generic group association schemes have been
studied in great details, where the transition amplitudes are given in terms of
characters of groups. Further investigated examples are the walk on graphs of
association schemes of symmetric , Dihedral and cyclic groups.
Also, following Ref.\cite{js}, the spectral distributions connected to the
highest irreducible representations of Terwilliger algebras of some rather
important graphs, namely distance regular graphs, have been presented. Then
using spectral distribution, the amplitudes of continuous-time quantum walk on
graphs such as cycle graph , Johnson and normal subgroup graphs have been
evaluated. {\bf Keywords: Continuous-time quantum walk, Association scheme,
Bose-Mesner algebra, Terwilliger algebra, Spectral distribution, Distance
regular graph.} {\bf PACs Index: 03.65.Ud}Comment: 44 pages, 4 figure
A Measure of Non-Markovianity for Unital Quantum Dynamical Maps
One of the most important topics in the study of the dynamics of open quantum
system is information exchange between system and environment. Based on the
features of a back-flow information from an environment to a system, an
approach is provided to detect non-Markovianity for unital dynamical maps. The
method takes advantage of non-contractive property of the von Neumann entropy
under completely positive and trace preserving unital maps. Accordingly, for
the dynamics of a single qubit as an open quantum system, the sign of the
time-derivative of the density matrix eigenvalues of the system determines the
non-Markovianity of unital quantum dynamical maps. The main characteristics of
the measure is to make the corresponding calculations and optimization
procedure simpler.Comment: 7 pages, 4 figures. Add new comments and new co-autho
Noisy Metrology: A saturable lower bound on quantum Fisher information
In order to provide a guaranteed precision and a more accurate judgement
about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an
upper bound (equivalently a lower bound on the quantum Fisher information) for
precision of estimation is introduced. Unlike the bounds previously introduced
in the literature, the upper bound is saturable and yields a practical
instruction to estimate the parameter through preparing the optimal initial
state and optimal measurement. The bound is based on the underling dynamics and
its calculation is straightforward and requires only the matrix representation
of the quantum maps responsible for encoding the parameter. This allows us to
apply the bound to open quantum systems whose dynamics are described by either
semigroup or non-semigroup maps. Reliability and efficiency of the method to
predict the ultimate precision limit are demonstrated by {three} main examples.Comment: 7 pages, 2 figure
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