87 research outputs found
Two-qubit correlations revisited: average mutual information, relevant (and useful) observables and an application to remote state preparation
Understanding how correlations can be used for quantum communication
protocols is a central goal of quantum information science. While many authors
have linked global measures of correlations such as entanglement or discord to
the performance of specific protocols, in general the latter may require only
correlations between specific observables. In this work, we first introduce a
general measure of correlations for two-qubit states based on the classical
mutual information between local observables. We then discuss the role of the
symmetry in the state's correlations distribution and accordingly provide a
classification of maximally mixed marginals states (MMMS). We discuss the
complementarity relation between correlations and coherence. By focusing on a
simple yet paradigmatic example, i.e., the remote state preparation protocol,
we introduce a method to systematically define proper protocol-tailored
measures of correlations. The method is based on the identification of those
correlations that are relevant (useful) for the protocol. The approach allows
on one hand to discuss the role of the symmetry of the correlations
distribution in determining the efficiency of the protocol, both for MMMS and
general two-qubit quantum states, and on the other hand to devise an optimized
protocol for non-MMMS that can have a better efficiency with respect to the
standard one. The scheme we propose can be extended to other communication
protocols and more general bipartite settings. Overall our findings clarify how
the key resources in simple communication protocols are the purity of the state
used and the symmetry of correlations distribution.Comment: Revised Figures, improved notation and clearer text to better
highlight the main finding
Global coherence of quantum evolutions based on decoherent histories: theory and application to photosynthetic quantum energy transport
Assessing the role of interference in natural and artificial quantum
dyanamical processes is a crucial task in quantum information theory. To this
aim, an appopriate formalism is provided by the decoherent histories framework.
While this approach has been deeply explored from different theoretical
perspectives, it still lacks of a comprehensive set of tools able to concisely
quantify the amount of coherence developed by a given dynamics. In this paper
we introduce and test different measures of the (average) coherence present in
dissipative (Markovian) quantum evolutions, at various time scales and for
different levels of environmentally induced decoherence. In order to show the
effectiveness of the introduced tools, we apply them to a paradigmatic quantum
process where the role of coherence is being hotly debated: exciton transport
in photosynthetic complexes. To spot out the essential features that may
determine the performance of the transport we focus on a relevant trimeric
subunit of the FMO complex and we use a simplified (Haken-Strobl) model for the
system-bath interaction. Our analysis illustrates how the high efficiency of
environmentally assisted transport can be traced back to a quantum recoil
avoiding effect on the exciton dynamics, that preserves and sustains the
benefits of the initial fast quantum delocalization of the exciton over the
network. Indeed, for intermediate levels of decoherence, the bath is seen to
selectively kill the negative interference between different exciton pathways,
while retaining the initial positive one. The concepts and tools here developed
show how the decoherent histories approach can be used to quantify the relation
between coherence and efficiency in quantum dynamical processes.Comment: 13 papges, 9 figure
Non-Gaussian quantum discord for Gaussian states
In recent years the paradigm based on entanglement as the unique measure of
quantum correlations has been challenged by the rise of new correlation
concepts, such as quantum discord, able to reveal quantum correlations that are
present in separable states. It is in general difficult to compute quantum
discord, because it involves a minimization over all possible local
measurements in a bipartition. In the realm of continuous variable (CV)
systems, a Gaussian version of quantum discord has been put forward upon
restricting to Gaussian measurements. It is natural to ask whether non-Gaussian
measurements can lead to a stronger minimization than Gaussian ones. Here we
focus on two relevant classes of two-mode Gaussian states: squeezed thermal
states (STS) and mixed thermal states (MTS), and allow for a range of
experimentally feasible non-Gaussian measurements, comparing the results with
the case of Gaussian measurements. We provide evidence that Gaussian
measurements are optimal for Gaussian states.Comment: 12 pages, 9 figures (3 appendices
Algebraic synthesis of time-optimal unitaries in SU(2) with alternating controls
We present an algebraic framework to study the time-optimal synthesis of
arbitrary unitaries in SU(2), when the control set is restricted to rotations
around two non-parallel axes in the Bloch sphere. Our method bypasses commonly
used control-theoretical techniques, and easily imposes necessary conditions on
time-optimal sequences. In a straightforward fashion, we prove that
time-optimal sequences are solely parametrized by three rotation angles and
derive general bounds on those angles as a function of the relative rotation
speed of each control and the angle between the axes. Results are substantially
different whether both clockwise and counterclockwise rotations about the given
axes are allowed, or only clockwise rotations. In the first case, we prove that
any finite time-optimal sequence is composed at most of five control
concatenations, while for the more restrictive case, we present scaling laws on
the maximum length of any finite time-optimal sequence. The bounds we find for
both cases are stricter than previously published ones and severely constrain
the structure of time-optimal sequences, allowing for an efficient numerical
search of the time-optimal solution. Our results can be used to find the
time-optimal evolution of qubit systems under the action of the considered
control set, and thus potentially increase the number of realizable unitaries
before decoherence
The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel
We address the degradation of continuous variable (CV) entanglement in a
noisy channel focusing on the set of photon-number entangled states. We exploit
several separability criteria and compare the resulting separation times with
the value of non-Gaussianity at any time, thus showing that in the
low-temperature regime: i) non-Gaussianity is a bound for the relative entropy
of entanglement and ii) Simon' criterion provides a reliable estimate of the
separation time also for nonGaussian states. We provide several evidences
supporting the conjecture that Gaussian entanglement is the most robust against
noise, i.e. it survives longer than nonGaussian one, and that this may be a
general feature for CV systems in Markovian channels.Comment: revised version, title and figures change
Stroke-related alterations in inter-areal communication
Beyond causing local ischemia and cell damage at the site of injury, stroke strongly affects long-range anatomical connections, perturbing the functional organization of brain networks. Several studies reported functional connectivity abnormalities parallelling both behavioral deficits and functional recovery across different cognitive domains. FC alterations suggest that long-range communication in the brain is altered after stroke. However, standard FC analyses cannot reveal the directionality and time scale of inter-areal information transfer. We used resting-state fMRI and covariance-based Granger causality analysis to quantify network-level information transfer and its alteration in stroke. Two main large-scale anomalies were observed in stroke patients. First, inter-hemispheric information transfer was significantly decreased with respect to healthy controls. Second, stroke caused inter-hemispheric asymmetries, as information transfer within the affected hemisphere and from the affected to the intact hemisphere was significantly reduced. Both anomalies were more prominent in resting-state networks related to attention and language, and they correlated with impaired performance in several behavioral domains. Overall, our findings support the hypothesis that stroke provokes asymmetries between the affected and spared hemisphere, with different functional consequences depending on which hemisphere is lesioned
Topology and energy transport in networks of interacting photosynthetic complexes
We address the role of topology in the energy transport process that occurs
in networks of photosynthetic complexes. We take inspiration from light
harvesting networks present in purple bacteria and simulate an incoherent
dissipative energy transport process on more general and abstract networks,
considering both regular structures (Cayley trees and hyperbranched fractals)
and randomly-generated ones. We focus on the the two primary light harvesting
complexes of purple bacteria, i.e., the LH1 and LH2, and we use
network-theoretical centrality measures in order to select different LH1
arrangements. We show that different choices cause significant differences in
the transport efficiencies, and that for regular networks centrality measures
allow to identify arrangements that ensure transport efficiencies which are
better than those obtained with a random disposition of the complexes. The
optimal arrangements strongly depend on the dissipative nature of the dynamics
and on the topological properties of the networks considered, and depending on
the latter they are achieved by using global vs. local centrality measures. For
randomly-generated networks a random arrangement of the complexes already
provides efficient transport, and this suggests the process is strong with
respect to limited amount of control in the structure design and to the
disorder inherent in the construction of randomly-assembled structures.
Finally, we compare the networks considered with the real biological networks
and find that the latter have in general better performances, due to their
higher connectivity, but the former with optimal arrangements can mimic the
real networks' behaviour for a specific range of transport parameters. These
results show that the use of network-theoretical concepts can be crucial for
the characterization and design of efficient artificial energy transport
networks.Comment: 14 pages, 16 figures, revised versio
Quantum Brachistochrone Curves as Geodesics: Obtaining Accurate Minimum-Time Protocols for the Control of Quantum Systems
Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.National Science Foundation (U.S.) (Project PHY-1005571)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-11-1-0268)National Science Foundation (U.S.) (Project CCF-1350397
Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning
Many real-world optimization problems contain unknown parameters that must be
predicted prior to solving. To train the predictive machine learning (ML)
models involved, the commonly adopted approach focuses on maximizing predictive
accuracy. However, this approach does not always lead to the minimization of
the downstream task loss. Decision-focused learning (DFL) is a recently
proposed paradigm whose goal is to train the ML model by directly minimizing
the task loss. However, state-of-the-art DFL methods are limited by the
assumptions they make about the structure of the optimization problem (e.g.,
that the problem is linear) and by the fact that can only predict parameters
that appear in the objective function. In this work, we address these
limitations by instead predicting \textit{distributions} over parameters and
adopting score function gradient estimation (SFGE) to compute decision-focused
updates to the predictive model, thereby widening the applicability of DFL. Our
experiments show that by using SFGE we can: (1) deal with predictions that
occur both in the objective function and in the constraints; and (2)
effectively tackle two-stage stochastic optimization problems
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