Decoherence effect on quantum-memory-assisted entropic uncertainty relations

Uncertainty principle significantly provides a bound to predict precision of measurement with regard to any two incompatible observables, and thereby plays a nontrivial role in quantum precision measurement. In this work, we observe the dynamical features of the quantum-memory-assisted entropic uncertainty relations (EUR) for a pair of incompatible measurements in an open system characterized by local generalized amplitude damping (GAD) noises. Herein, we derive the dynamical evolution of the entropic uncertainty with respect to the measurement affecting by the canonical GAD noises when particle A is initially entangled with quantum memory B. Specifically, we examine the dynamics of EUR in the frame of three realistic scenarios: one case is that particle A is affected by environmental noise (GAD) while particle B as quantum memory is free from any noises, another case is that particle B is affected by the external noise while particle A is not, and the last case is that both of the particles suffer from the noises. By analytical methods, it turns out that the uncertainty is not full dependent of quantum correlation evolution of the composite system consisting of A and B, but the minimal conditional entropy of the measured subsystem. Furthermore, we present a possible physical interpretation for the behavior of the uncertainty evolution by means of the mixedness of the observed system; we argue that the uncertainty might be dramatically correlated with the systematic mixedness. Furthermore, we put forward a simple and effective strategy to reduce the measuring uncertainty of interest upon quantum partially collapsed measurement. Therefore, our explorations might offer an insight into the dynamics of the entropic uncertainty relation in a realistic system, and be of importance to quantum precision measurement during quantum information processing.     

Thermodynamically equivalent silicon models of voltage-dependent ion channels

We model ion channels in silicon by exploiting similarities between the thermodynamic principles that govern ion channels and those that govern transistors. Using just eight transistors, we replicate--for the first time in silicon--the sigmoidal voltage dependence of activation (or inactivation) and the bell-shaped voltage-dependence of its time constant. We derive equations describing the dynamics of our silicon analog and explore its flexibility by varying various parameters. In addition, we validate the design by implementing a channel with a single activation variable. The design's compactness allows tens of thousands of copies to be built on a single chip, facilitating the study of biologically realistic models of neural computation at the network level in silicon.     

Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations

In this work, we investigate the dynamic features of the entropic uncertainty for two incompatible measurements under local unital and nonunital channels. Herein, we choose Pauli operators \(\sigma _x \) and \(\sigma _z \) as a pair of observables of interest measuring on particle A, and the uncertainty can be predicted when particle A is entangled with quantum memory B. We explore the dynamics of the uncertainty for the measurement under local unitary (phase-damping) and nonunitary (amplitude-damping) channels, respectively. Remarkably, we derive the entropic uncertainty relation under three different kinds of measurements of Pauli-observable pair under various realistic noisy environments; it has been found that the entropic uncertainty has the same tendency of its evolution during the AD and PD channel when we choose \(\sigma _x \) and \(\sigma _y \) measurement. Besides, we find out that the entropic uncertainty will have an optimal value if one chooses \(\sigma _x \) and \(\sigma _z \) as the measurement incompatibility, comparing with others. Furthermore, in order to reduce the entropic uncertainty in noisy environment, we propose an effective strategy to steer the amount by means of implementing a filtering operation on the particle under the two types of channels, respectively. It turns out that this operation can greatly reduce the entropic uncertainty by modulation of the operation strength. Thus, our investigations might offer an insight into the dynamics and steering of the entropic uncertainty in an open system.     

Uncertainty of transfer function modelling using prior estimated noise models

Assuming “small” model errors (unmodelled dynamics and/or nonlinear distortions) and “large” signal-to-noise ratios we derive in this paper explicit expressions for the covariance matrix of a frequency domain estimator using prior estimated noise models. These analytic expressions (i) give a clear insight in the behaviour of the covariance matrix as a function of the signal-to-noise ratio, the unmodelled dynamics and the nonlinear distortions, and (ii) allow to predict accurately the order of magnitude of the actual uncertainty of the estimates. The link with the classical prediction error approach is also established.     

Uncertainty under quantum measures and quantum memory

The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty relation will vary. Based on the knowledge of correlations between the measured particle and quantum memory, we have investigated the entropic uncertainty relations for two and multiple measurements and generalized the lower bounds on the sum of Shannon entropies without quantum side information to those that allow quantum memory. In particular, we have obtained generalization of Kaniewski–Tomamichel–Wehner’s bound for effective measures and majorization bounds for noneffective measures to allow quantum side information. Furthermore, we have derived several strong bounds for the entropic uncertainty relations in the presence of quantum memory for two and multiple measurements. Finally, potential applications of our results to entanglement witnesses are discussed via the entropic uncertainty relation in the absence of quantum memory.     

Probing entropic uncertainty relations under a two-atom system coupled with structured bosonic reservoirs

The uncertainty principle imposes constraints on an observer’s ability to make precision measurements for two incompatible observables; thus, uncertainty relations play a key role in quantum precision measurement in the field of quantum information science. Here, our aim is to examine non-Markovian effects on quantum-memory-assisted entropic uncertainty relations in a system consisting of two atoms coupled with structured bosonic reservoirs. Explicitly, we explore the dynamics of the uncertainty relations via entropic measures in non-Markovian regimes when two atomic qubits independently interact with their own infinite degree-of-freedom bosonic reservoir. We show that measurement uncertainty vibrates with periodically increasing amplitude with growing non-Markovianity of the observed system and ultimately saturates toward a fixed value at a long time limit. It is worth noting that there are several appealing conclusions raised by us: First, the uncertainty’s lower bound does not entirely depend on the quantum correlations within the two-qubit system, being affected by an interplay between the quantum discord and the minimal von Neumann conditional entropy \(\mathcal{S}_\mathrm{ce}\). Second, the dynamic characteristic of the measurement uncertainty is considerably distinctive with regard to Markovian and non-Markovian regimes, respectively. Third, the measurement uncertainty is closely correlated with the Bell non-locality \({\mathcal{B}}\). Moreover, we claim that the entropic uncertainty relation could be a promising tool with which to probe entanglement in current architecture.     

Renormalization of global entanglement and Bell nonlocality in the Ising model with a transverse field

By combining quantum renormalization group approach and critical theory, we investigate the performance of global entanglement and Bell nonlocality in quantum phase transition (QPT) that occurred in Ising model with a transverse field (ITF). After several iterations, both of them gradually develop two different saturated values relevant to the Ising phase and paramagnetic phase. Moreover, we proved that the inherent block–block correlation is strong enough to violate the quantum nonlocality. What is more, we derive an exact relation between global entanglement and Bell nonlocality for the given case. To serve further insight, the nonanalytic and scaling behaviors are analyzed.     

State-independent uncertainty relations and entanglement detection

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N-dimensional observables. The uncertainty relation for the incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn’s conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.     

Entanglement mean field theory: Lipkin–Meshkov–Glick Model

Entanglement mean field theory is an approximate method for dealing with many-body systems, especially for the prediction of the onset of phase transitions. While previous studies have concentrated mainly on applications of the theory on short-range interaction models, we show here that it can be efficiently applied also to systems with long-range interaction Hamiltonians. We consider the (quantum) Lipkin–Meshkov–Glick spin model, and derive the entanglement mean field theory reduced Hamiltonian. A similar recipe can be applied to obtain entanglement mean field theory reduced Hamiltonians corresponding to other long-range interaction systems. We show, in particular, that the zero temperature quantum phase transition present in the Lipkin–Meshkov–Glick model can be accurately predicted by the theory.     

Noise effects on entanglement distribution by separable state

We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models, we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two-qubit/qudit and three-qubit entangled states. In explicit examples of the noise family, we show that there exists a critical value of noise parameter beyond which distribution of distillable entanglement is not possible. Furthermore, we determine how this critical value increases in terms of Hilbert space dimension, when distributing d-dimensional Bell states.     

Enhancement of genuine multipartite entanglement and purity of three qubits under decoherence via bang–bang pulses with finite period

We propose a scheme to control the dynamics of genuine multipartite entanglement and purity of qubits within spatially separated thermal baths using the bang–bang pulses with finite period. The qubits are initially entangled and have no direct interactions. The genuine multipartite entanglement of the system is measured by an entanglement monotone based on a generalization of the Peres–Horodecki criterion to multipartite systems. We first derive a master equation to describe the non-Markovian dynamics of an arbitrary number of qubits within their baths with decoherence and dynamical decoupling. Then, we calculate the entanglement monotone and purity of three qubits in super-Ohmic, sub-Ohmic, and Ohmic baths numerically. The effects of the period of pulses on the non-Markovian dynamics of qubits are discussed. We show the genuine multipartite entanglement and purity can be simultaneously improved by applying the bang–bang pulses with finite period. In particular, the bang–bang pulses with finite period are more efficient when the qubits are put into the sub-Ohmic or Ohmic baths than the case of the super-Ohmic bath.     

Reinforcement learning, spike-time-dependent plasticity, and the BCM rule

Learning agents, whether natural or artificial, must update their internal parameters in order to improve their behavior over time. In reinforcement learning, this plasticity is influenced by an environmental signal, termed a reward, that directs the changes in appropriate directions. We apply a recently introduced policy learning algorithm from machine learning to networks of spiking neurons and derive a spike-time-dependent plasticity rule that ensures convergence to a local optimum of the expected average reward. The approach is applicable to a broad class of neuronal models, including the Hodgkin-Huxley model. We demonstrate the effectiveness of the derived rule in several toy problems. Finally, through statistical analysis, we show that the synaptic plasticity rule established is closely related to the widely used BCM rule, for which good biological evidence exists.     

Dynamics of quantum entanglement in quantum channels

Based on the von Neumann entropy, we give a computational formalism of the quantum entanglement dynamics in quantum channels, which can be applied to a general finite systems coupled with their environments in quantum channels. The quantum entanglement is invariant in the decoupled local unitary quantum channel, but it is variant in the non-local coupled unitary quantum channel. The numerical investigation for two examples, two-qubit and two-qutrit models, indicates that the quantum entanglement evolution in the quantum non-local coupling channel oscillates with the coupling strength and time, and depends on the quantum entanglement of the initial state. It implies that quantum information loses or gains when the state of systems evolves in the quantum non-local coupling channel.     

Bayesian model assessment and comparison using cross-validation predictive densities

In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate because it describes the uncertainty in the estimate. The distributions of the expected utility estimates can also be used to compare models, for example, by computing the probability of one model having a better expected utility than some other model. We propose an approach using cross-validation predictive densities to obtain expected utility estimates and Bayesian bootstrap to obtain samples from their distributions. We also discuss the probabilistic assumptions made and properties of two practical cross-validation methods, importance sampling and k-fold cross-validation. As illustrative examples, we use multilayer perceptron neural networks and gaussian processes with Markov chain Monte Carlo sampling in one toy problem and two challenging real-world problems.     

Distributed extended object tracking information filter over sensor networks

This work aims to design a distributed extended object tracking system over a realistic network, where both the extent and kinematics are required to retain consensus within the entire network. To this end, we resort to the multiplicative error model (MEM) that allows the extent parameters of perpendicular axis-symmetric objects to have individual uncertainty. To incorporate the MEM into the information filter (IF) style, we use the moment-matching technique to derive two pair linear models with only additive noise. The separation is merely in a fashion, and the cross-correlation between states is preserved as parameters in each other's model. As a result, the closed-form expressions are transferred into an alternating iteration of two linear IFs. With the two models, a centralized IF is proposed wherein the measurements are converted into a summation of innovation parts. Later, under a sensor network with the communication nodes and sensor nodes, we present two distributed IFs through the consensus on information and consensus on measurement schemes, respectively. Moreover, we prove the estimation errors of the proposed filter are exponentially bounded in the mean square. The benefits are testified by numerical experiments in comparison to state-of-the-art filters in literature.     

The general optimal market area model with uncertain and nonstationary demand

Facility location problems involve determining the number of facilities to open, the location of facilities, and the market area that each facility will serve. While the environment is seldom stable, algorithms for solving models that incorporate change and uncertainty are rare and limited in scope. Consequently, the common approach in practice is to use algorithms for static models with perhaps some scenario analysis to accommodate change and uncertainty. We introduce an analytically tractable model that includes dynamic and uncertain demand. By studying how the model can be solved by solving a related model with stationary demand, we are able to derive guidelines on how to apply static analysis tools to problems with dynamic demand. While the analysis is contingent upon the underlying model, evidence on the model's robustness suggests that the results represent plausible guidelines for problems that extend well beyond the model.     

Assessment of the different sources of uncertainty in a SWAT model of the River Senne (Belgium)

Although rainfall input uncertainties are widely identified as being a key factor in hydrological models, the rainfall uncertainty is typically not included in the parameter identification and model output uncertainty analysis of complex distributed models such as SWAT and in maritime climate zones. This paper presents a methodology to assess the uncertainty of semi-distributed hydrological models by including, in addition to a list of model parameters, additional unknown factors in the calibration algorithm to account for the rainfall uncertainty (using multiplication factors for each separately identified rainfall event) and for the heteroscedastic nature of the errors of the stream flow. We used the Differential Evolution Adaptive Metropolis algorithm (DREAM_(zs)) to infer the parameter posterior distributions and the output uncertainties of a SWAT model of the River Senne (Belgium). Explicitly considering heteroscedasticity and rainfall uncertainty leads to more realistic parameter values, better representation of water balance components and prediction uncertainty intervals.     

Modelling opinion formation driven communities in social networks

In a previous paper we proposed a model to study the dynamics of opinion formation in human societies by a co-evolution process involving two distinct time scales of fast transaction and slower network evolution dynamics. In the transaction dynamics we take into account short range interactions as discussions between individuals and long range interactions to describe the attitude to the overall mood of society. The latter is handled by a uniformly distributed parameter α, assigned randomly to each individual, as quenched personal bias. The network evolution dynamics is realised by rewiring the societal network due to state variable changes as a result of transaction dynamics. The main consequence of this complex dynamics is that communities emerge in the social network for a range of values in the ratio between time scales. In this paper we focus our attention on the attitude parameter α and its influence on the conformation of opinion and the size of the resulting communities. We present numerical studies and extract interesting features of the model that can be interpreted in terms of social behaviour.     

Exploiting Kondo spin chains for generating long range distance independent entanglement

We investigate the entanglement properties of the Kondo spin chain when it is prepared in its ground state as well as its dynamics following a single bond quench. We show that a true measure of entanglement such as negativity enables to characterize the unique features of the gapless Kondo regime. We determine the spatial extent of the Kondo screening cloud and propose an ansatz for the ground state in the Kondo regime accessible to this spin chain; we also demonstrate that the impurity spin is indeed maximally entangled with the Kondo cloud. We exploit these features of the entanglement in the gapless Kondo regime to show that a single local quench at one end of a Kondo spin chain may always induce a fast and long lived oscillatory dynamics, which establishes a high quality entanglement between the individual spins at the opposite ends of the chain. This entanglement is a footprint of the presence of the Kondo cloud and may be engineered so as to attain—even for very large chains—a constant high value independent of the length; in addition, it is thermally robust. Moreover, we show that high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. To better evidence the remarkable peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin chain model in the gapped dimerised regime where these remarkable features are absent.     

Dynamics of tripartite quantum correlations and decoherence in flux qubit systems under local and non-local static noise

We investigate the dynamics of entanglement, decoherence and quantum discord in a system of three non-interacting superconducting flux qubits (fqubits) initially prepared in a Greenberger–Horne–Zeilinger (GHZ) state and subject to static noise in different, bipartite and common environments, since it is recognized that different noise configurations generally lead to completely different dynamical behavior of physical systems. The noise is modeled by randomizing the single fqubit transition amplitude. Decoherence and quantum correlations dynamics are strongly affected by the purity of the initial state, type of system–environment interaction and the system–environment coupling strength. Specifically, quantum correlations can persist when the fqubits are commonly coupled to a noise source, and reaches a saturation value respective to the purity of the initial state. As the number of decoherence channels increases (bipartite and different environments), decoherence becomes stronger against quantum correlations that decay faster, exhibiting sudden death and revival phenomena. The residual entanglement can be successfully detected by means of suitable entanglement witness, and we derive a necessary condition for entanglement detection related to the tunable and non-degenerated energy levels of fqubits. In accordance with the current literature, our results further suggest the efficiency of fqubits over ordinary ones, as far as the preservation of quantum correlations needed for quantum processing purposes is concerned.