4,867 research outputs found
Non-Markovian generalization of the Lindblad theory of open quantum systems
A systematic approach to the non-Markovian quantum dynamics of open systems
is given by the projection operator techniques of nonequilibrium statistical
mechanics. Combining these methods with concepts from quantum information
theory and from the theory of positive maps, we derive a class of correlated
projection superoperators that take into account in an efficient way
statistical correlations between the open system and its environment. The
result is used to develop a generalization of the Lindblad theory to the regime
of highly non-Markovian quantum processes in structured environments.Comment: 10 pages, 1 figure, replaced by published versio
Witness for initial system-environment correlations in open system dynamics
We study the evolution of a general open quantum system when the system and
its environment are initially correlated. We show that the trace distance
between two states of the open system can increase above its initial value, and
derive tight upper bounds for the growth of the distinguishability of open
system states. This represents a generalization of the contraction property of
quantum dynamical maps. The obtained inequalities can be interpreted in terms
of the exchange of information between the system and the environment, and lead
to a witness for system-environment correlations which can be determined
through measurements on the open system alone.Comment: 4 pages, 1 figur
New method to simulate quantum interference using deterministic processes and application to event-based simulation of quantum computation
We demonstrate that networks of locally connected processing units with a
primitive learning capability exhibit behavior that is usually only attributed
to quantum systems. We describe networks that simulate single-photon
beam-splitter and Mach-Zehnder interferometer experiments on a causal,
event-by-event basis and demonstrate that the simulation results are in
excellent agreement with quantum theory. We also show that this approach can be
generalized to simulate universal quantum computers.Comment: J. Phys. Soc. Jpn. (in press) http://www.compphys.net/dl
Stochastic wave function method for non-Markovian quantum master equations
A generalization of the stochastic wave function method to quantum master
equations which are not in Lindblad form is developed. The proposed stochastic
unravelling is based on a description of the reduced system in a doubled
Hilbert space and it is shown, that this method is capable of simulating
quantum master equations with negative transition rates. Non-Markovian effects
in the reduced systems dynamics can be treated within this approach by
employing the time-convolutionless projection operator technique. This ansatz
yields a systematic perturbative expansion of the reduced systems dynamics in
the coupling strength. Several examples such as the damped Jaynes Cummings
model and the spontaneous decay of a two-level system into a photonic band gap
are discussed. The power as well as the limitations of the method are
demonstrated.Comment: RevTex, 14 pages, 9 figures, uses multico
Time-convolutionless master equation for quantum dots: Perturbative expansion to arbitrary order
The master equation describing the non-equilibrium dynamics of a quantum dot
coupled to metallic leads is considered. Employing a superoperator approach, we
derive an exact time-convolutionless master equation for the probabilities of
dot states, i.e., a time-convolutionless Pauli master equation. The generator
of this master equation is derived order by order in the hybridization between
dot and leads. Although the generator turns out to be closely related to the
T-matrix expressions for the transition rates, which are plagued by
divergences, in the time-convolutionless generator all divergences cancel order
by order. The time-convolutionless and T-matrix master equations are contrasted
to the Nakajima-Zwanzig version. The absence of divergences in the
Nakajima-Zwanzig master equation due to the nonexistence of secular reducible
contributions becomes rather transparent in our approach, which explicitly
projects out these contributions. We also show that the time-convolutionless
generator contains the generator of the Nakajima-Zwanzig master equation in the
Markov approximation plus corrections, which we make explicit. Furthermore, it
is shown that the stationary solutions of the time-convolutionless and the
Nakajima-Zwanzig master equations are identical. However, this identity neither
extends to perturbative expansions truncated at finite order nor to dynamical
solutions. We discuss the conditions under which the Nakajima-Zwanzig-Markov
master equation nevertheless yields good results.Comment: 13 pages + appendice
Phonon-induced dephasing of singlet-triplet superpositions in double quantum dots without spin-orbit coupling
We show that singlet-triplet superpositions of two-electron spin states in a
double quantum dot undergo a phonon-induced pure dephasing which relies only on
the tunnel coupling between the dots and on the Pauli exclusion principle. As
such, this dephasing process is independent of spin-orbit coupling or hyperfine
interactions. The physical mechanism behind the dephasing is elastic phonon
scattering, which persists to much lower temperatures than real phonon-induced
transitions. Quantitative calculations performed for a lateral GaAs/AlGaAs
gate-defined double quantum dot yield micro-second dephasing times at
sub-Kelvin temperatures, which is consistent with experimental observations.Comment: Extended versio
Quantum Transport through Nanostructures with Orbital Degeneracies
Geometric symmetries cause orbital degeneracies in a molecule's spectrum. In
a single-molecule junction, these degeneracies are lifted by various
symmetry-breaking effects. We study quantum transport through such
nanostructures with an almost degenerate spectrum. We show that the master
equation for the reduced density matrix must be derived within the
singular-coupling limit as opposed to the conventional weak-coupling limit.
This results in signatures of the density matrix's off-diagonal elements in the
transport characteristics
On the Contractivity of Hilbert-Schmidt distance under open system dynamics
We show that the Hilbert-Schmidt distance, unlike the trace distance, between
quantum states is generally not monotonic for open quantum systems subject to
Lindblad semigroup dynamics. Sufficient conditions for contractivity of the
Hilbert-Schmidt norm in terms of the dissipation generators are given. Although
these conditions are not necessary, simulations suggest that non-contractivity
is the typical case, i.e., that systems for which the Hilbert-Schmidt distance
between quantum states is monotonically decreasing form only a small set of all
possible dissipative systems for N>2, in contrast to the case N=2 where the
Hilbert-Schmidt distance is always monotonically decreasing.Comment: Major revision. We would particularly like to thank D Perez-Garcia
for constructive feedbac
Optimal entanglement criterion for mixed quantum states
We develop a strong and computationally simple entanglement criterion. The
criterion is based on an elementary positive map Phi which operates on state
spaces with even dimension N >= 4. It is shown that Phi detects many entangled
states with positive partial transposition (PPT) and that it leads to a class
of optimal entanglement witnesses. This implies that there are no other
witnesses which can detect more entangled PPT states. The map Phi yields a
systematic method for the explicit construction of high-dimensional manifolds
of bound entangled states.Comment: 4 pages, no figures, replaced by published version (minor changes),
Journal-reference adde
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