36 research outputs found
Comparing different non-Markovianity measures: A case study
We consider two recently proposed measures of non-Markovianity applied to a
particular quantum process describing the dynamics of a driven qubit in a
structured reservoir. The motivation of this study is twofold: on one hand, we
study the differences and analogies of the non-Markovianity measures and on the
other hand, we investigate the effect of the driving force on the dissipative
dynamics of the qubit. In particular we ask if the drive introduces new
channels for energy and/or information transfer between the system and the
environment, or amplifies existing ones. We show under which conditions the
presence of the drive slows down the inevitable loss of quantum properties of
the qubit.Comment: 5 pages, no figures. Published version with minor modification
Quantum switching networks for perfect qubit routing
We develop the work of Christandl et al. [M. Christandl, N. Datta, T. C.
Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Phys. Rev. A 71, 032312 (2005)],
to show how a d-hypercube homogenous network can be dressed by additional links
to perfectly route quantum information between any given input and output nodes
in a duration which is independent of the routing chosen and, surprisingly,
size of the network
Markovian evolution of strongly coupled harmonic oscillators
We investigate how to model Markovian evolution of coupled harmonic
oscillators, each of them interacting with a local environment. When the
coupling between the oscillators is weak, dissipation may be modeled using
local Lindblad terms for each of the oscillators in the master equation, as is
commonly done. When the coupling between oscillators is strong, this model may
become invalid. We derive a master equation for two coupled harmonic
oscillators which are subject to individual heat baths modeled by a collection
of harmonic oscillators, and show that this master equation in general contains
non-local Lindblad terms. We compare the resulting time evolution with that
obtained for dissipation through local Lindblad terms for each individual
oscillator, and show that the evolution is different in the two cases. In
particular, the two descriptions give different predictions for the steady
state and for the entanglement between strongly coupled oscillators. This shows
that when describing strongly coupled harmonic oscillators, one must take great
care in how dissipation is modeled, and that a description using local Lindblad
terms may fail. This may be particularly relevant when attempting to generate
entangled states of strongly coupled quantum systems.Comment: 11 pages, 4 figures, significantly revised and close to the published
versio
Decoherence-free quantum information in the presence of dynamical evolution
We analyze decoherence-free (DF) quantum information in the presence of an
arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a
Markovian master equation. We show that the most appropriate encoding for N
qubits is probably contained within the ~(2/9) N excitation subspace. We give a
timescale over which one would expect to apply other methods to correct for the
system Hamiltonian. In order to remain applicable to experiment, we then focus
on small systems, and present examples of DF quantum information for three and
four qubits. We give an encoding for four qubits that, while quantum
information remains in the two-excitation subspace, protects against an
arbitrary bath-induced system Hamiltonian. Although our results are general to
any system of qubits that satisfies our assumptions, throughout the paper we
use dipole-coupled qubits as an example physical system.Comment: 8 pages, 4 figure
Super- and subradiant emission of two-level systems in the near-Dicke limit
We analyze the stability of super- and subradiant states in a system of
identical two-level atoms in the near-Dicke limit, i.e., when the atoms are
very close to each other compared to the wavelength of resonant light. The
dynamics of the system are studied using a renormalized master equation, both
with multipolar and minimal-coupling interaction schemes. We show that both
models lead to the same result and, in contrast to unrenormalized models,
predict that the relative orientation of the (co-aligned) dipoles is
unimportant in the Dicke limit. Our master equation is of relevance to any
system of dipole-coupled two-level atoms, and gives bounds on the strength of
the dipole-dipole interaction for closely spaced atoms. Exact calculations for
small atom systems in the near-Dicke limit show the increased emission times
resulting from the evolution generated by the strong dipole-dipole interaction.
However, for large numbers of atoms in the near-Dicke limit, it is shown that
as the number of atoms increases, the effect of the dipole-dipole interaction
on collective emission is reduced.Comment: 14 pages, 6 figures, published versio
Geometric phase for an adiabatically evolving open quantum system
We derive an elegant solution for a two-level system evolving adiabatically
under the influence of a driving field with a time-dependent phase, which
includes open system effects such as dephasing and spontaneous emission. This
solution, which is obtained by working in the representation corresponding to
the eigenstates of the time-dependent Hermitian Hamiltonian, enables the
dynamic and geometric phases of the evolving density matrix to be separated and
relatively easily calculated.Comment: 10 pages, 0 figure
Canonical form of master equations and characterization of non-Markovianity
Master equations govern the time evolution of a quantum system interacting
with an environment, and may be written in a variety of forms. Time-independent
or memoryless master equations, in particular, can be cast in the well-known
Lindblad form. Any time-local master equation, Markovian or non-Markovian, may
in fact also be written in a Lindblad-like form. A diagonalisation procedure
results in a unique, and in this sense canonical, representation of the
equation, which may be used to fully characterize the non-Markovianity of the
time evolution. Recently, several different measures of non-Markovianity have
been presented which reflect, to varying degrees, the appearance of negative
decoherence rates in the Lindblad-like form of the master equation. We
therefore propose using the negative decoherence rates themselves, as they
appear in the canonical form of the master equation, to completely characterize
non-Markovianity. The advantages of this are especially apparent when more than
one decoherence channel is present. We show that a measure proposed by Rivas et
al. is a surprisingly simple function of the canonical decoherence rates, and
give an example of a master equation that is non-Markovian for all times t>0,
but to which nearly all proposed measures are blind. We also give necessary and
sufficient conditions for trace distance and volume measures to witness
non-Markovianity, in terms of the Bloch damping matrix.Comment: v2: Significant update, with many new results and one new author. 12
pages; v3: Minor clarifications, to appear in PRA; v4: matches published
versio
Quantum probability rule : a generalization of the theorems of Gleason and Busch
Buschs theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleasons theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory
Dynamics of correlations due to a phase noisy laser
We analyze the dynamics of various kinds of correlations present between two
initially entangled independent qubits, each one subject to a local phase noisy
laser. We give explicit expressions of the relevant quantifiers of correlations
for the general case of single-qubit unital evolution, which includes the case
of a phase noisy laser. Although the light field is treated as classical, we
find that this model can describe revivals of quantum correlations. Two
different dynamical regimes of decay of correlations occur, a Markovian one
(exponential decay) and a non-Markovian one (oscillatory decay with revivals)
depending on the values of system parameters. In particular, in the
non-Markovian regime, quantum correlations quantified by quantum discord show
an oscillatory decay faster than that of classical correlations. Moreover,
there are time regions where nonzero discord is present while entanglement is
zero.Comment: 7 pages, 3 figures, accepted for publication in Phys. Scripta,
special issue for CEWQO 2011 proceeding