95 research outputs found
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
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
Quantum speed limit time in the presence of disturbance
Quantum theory sets a bound on the minimal time evolution between initial and
target states. This bound is called as quantum speed limit time. It is used to
quantify maximal speed of quantum evolution. The quantum evolution will be
faster, if quantum speed limit time decreases. In this work, we study the
quantum speed limit time of a quantum state in the presence of disturbance
effects in an environment. We use the model which is provided by Masashi Ban in
\href{https://doi.org/10.1103/PhysRevA.99.012116}{Phys. Rev. A 99, 012116
(2019)}. In this model two quantum systems and
interact with environment sequentially. At first, quantum system
interacts with the environment as an auxiliary system then
quantum system interacts with disturbed environment immediately.
In this work, we consider dephasing coupling with two types of environment with
different spectral density: Ohmic and Lorentzian. We observe that,
non-Markovian effects will be appear in the dynamics of quantum system
by the interaction of quantum system with the
environment. Given the fact that quantum speed limit time reduces due to
non-Markovian effects, we show that disturbance effects will reduce the quantum
speed limit time.Comment: comments are welcome, 14 pages, 5 figure
Tunneling of conduction band electrons driven by a laser field in a double quantum dot: An open systems approach
In this paper, we investigate tunneling of conduction band electrons in a
system of an asymmetric double quantum dot which interacts with an environment.
First, we consider the case in which the system only interacts with the
environment and demonstrate that as time goes to infinity they both reach an
equilibrium, which is expected, and there is always a maximum and minimum for
the populations of the states of the system. Then we investigate the case in
which an external resonant optical pulse (a laser) is applied to the system
interacting with the environment. However, in this case for different
intensities we have different populations of the states in equilibrium and as
the intensity of the laser gets stronger, the populations of the states in
equilibrium approach the same constant.Comment: 8 pages, 13 figure
Tightening the tripartite quantum memory assisted entropic uncertainty relation
The uncertainty principle determines the distinction between the classical
and quantum worlds. This principle states that it is not possible to measure
two incompatible observables with the desired accuracy simultaneously. In
quantum information theory, Shannon entropy has been used as an appropriate
measure to express the uncertainty relation. According to the applications of
entropic uncertainty relation, studying and trying to improve the bound of this
relation is of great importance. Uncertainty bound can be altered by
considering an extra quantum system as the quantum memory which is
correlated with the measured quantum system . One can extend the bipartite
quantum memory assisted entropic uncertainty relation to tripartite quantum
memory assisted entropic uncertainty relation in which the memory is split into
two parts. In this work, we obtain a lower bound for the tripartite quantum
memory assisted entropic uncertainty relation. Our lower bound has two
additional terms compared to the lower bound in [Phys. Rev. Lett. 103, 020402
(2009)] which depending on the conditional von Neumann entropy, the Holevo
quantity and mutual information. It is shown that the bound obtained in this
work is more tighter than other bounds. In addition, using our lower bound, a
lower bound for the quantum secret key rate has been obtained. The lower bound
is also used to obtain the states for which the strong subadditivity inequality
and Koashi-Winter inequality is satisfied with equality.Comment: 6 pages, 4 figures, comments and suggestions are welcome
The entropy production of thermal operations
According to the first and second laws of thermodynamics and the definitions
of work and heat, microscopic expressions for the non-equilibrium entropy
production have been achieved. Recently, a redefinition of heat has been
presented in [\href{Nature Communicationsvolume 8, Article number: 2180
(2017)}{Nat. Commun. 8, 2180 (2017)}]. We are going to determine how this
redefinition of heat could affect the expression of the entropy production.
Utilizing this new definition of heat, it could be found out that there is a
new expression for the entropy production for thermal operations. It could be
derived if the initial state of the system and the bath is factorized, and if
the total entropy of composite system is preserved, then the new entropy
production will be equal to mutual information between the system and the bath.
It is shown that if the initial state of the system is diagonal in energy
bases, then the thermal operations cannot create a quantum correlation between
the system and the bath.Comment: 5 pages, 1 figure
Quantum Thermodynamic Force and Flow
Why do quantum evolutions occur and why do they stop at certain points? In
classical thermodynamics affinity was introduced to predict in which direction
an irreversible process proceeds. In this paper the quantum mechanical
counterpart of classical affinity is found. It is shown that the quantum
version of affinity can predict in which direction a process evolves. A new
version of the second law of thermodynamics is derived through quantum affinity
for energy-incoherent state interconversion under thermal operations. we will
also see that the quantum affinity can be a good candidate to be responsible,
as a force, for driving the flow and backflow of information in Markovian and
non-Markovian evolutions. Finally we show that the rate of quantum coherence
can be interpreted as the pure quantum mechanical contribution of the total
thermodynamic force and flow. Thus It is seen that, from a thermodynamic point
of view, any interaction from the outside with the system or any measurement on
the system may be represented by a quantum affinity.Comment: 8 pages, 4 figure
Time-invariant Discord: High Temperature Limit and Initial Environmental Correlations
We present a thorough investigation of the phenomena of frozen and
time-invariant quantum discord for two-qubit systems independently interacting
with local reservoirs. Our work takes into account several significant effects
present in decoherence models, which have not been yet explored in the context
of time-invariant quantum discord, but which in fact must be typically
considered in almost all realistic models. Firstly, we study the combined
influence of dephasing, dissipation and heating reservoirs at finite
temperature. Contrarily to previous claims in the literature, we show the
existence of time-invariant discord at high temperature limit in the weak
coupling regime, and also examine the effect of thermal photons on the
dynamical behaviour of frozen discord. Secondly, we explore the consequences of
having initial correlations between the dephasing reservoirs. We demonstrate in
detail how the time-invariant discord is modified depending on the relevant
system parameters such as the strength of the initial amount of entanglement
between the reservoirs.Comment: 10 pages, 7 figure
Quantum speed limit time for correlated quantum channel
Memory effects play a fundamental role in the dynamics of open quantum
systems. There exist two different views on memory for quantum noises. In the
first view, the quantum channel has memory when there exist correlations
between successive uses of the channels on a sequence of quantum systems. These
types of channels are also known as correlated quantum channels. In the second
view, memory effects result from correlations which are created during the
quantum evolution. In this work we will consider the first view and study the
quantum speed limit time for a correlated quantum channel. Quantum speed limit
time is the bound on the minimal time which is needed for a quantum system to
evolve from an initial state to desired states. The quantum evolution is fast
if the quantum speed limit time is short. In this work, we will study the
quantum speed limit time for some correlated unital and correlated non-unital
channels. As an example for unital channels we choose correlated dephasing
colored noise. We also consider the correlated amplitude damping and correlated
squeezed generalized amplitude damping channels as the examples for non-unital
channels. It will be shown that the quantum speed limit time for correlated
pure dephasing colored noise is increased by increasing correlation strength,
while for correlated amplitude damping and correlated squeezed generalized
amplitude damping channels quantum speed limit time is decreased by increasing
correlation strength.Comment: 16 pages, 3 figures, comments and suggestions are welcom
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