Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits tradeoffs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n). This ensures an intrinsic bound that is independent of the choice of parametrization

Semiparametric estimation of shifts on compact Lie groups for image registration

In this paper we focus on estimating the deformations that may exist between similar images in the presence of additive noise when a reference template is unknown. The deformations aremodeled as parameters lying in a finite dimensional compact Lie group. A generalmatching criterion based on the Fourier transformand itswell known shift property on compact Lie groups is introduced. M-estimation and semiparametric theory are then used to study the consistency and asymptotic normality of the resulting estimators. As Lie groups are typically nonlinear spaces, our tools rely on statistical estimation for parameters lying in a manifold and take into account the geometrical aspects of the problem. Some simulations are used to illustrate the usefulness of our approach and applications to various areas in image processing are discussed

Log-Distributional Approach for Learning Covariate Shift Ratios

Distributional Reinforcement Learning theory suggests that distributional fixed points could play a fundamental role to learning non additive value functions. In particular, we propose a distributional approach for learning Covariate Shift Ratios, whose update rule is originally multiplicative

New concepts in quantum-metrology: From coherent averaging to Hamiltonian extensions

This thesis is dedicated to the understanding of the metrology of quantum systems by using the tools of quantum parameter estimation, in particular the quantum Fisher information (QFI). Our first project deals with a specific protocol of quantum enhanced measurement known as coherent averaging [Braun and Martin, 2011]. This protocol is based on a star topology, with one central object, the so-called quantum bus, connected to N extra subsystems, called probes. For the estimation of a parameter characteristic of the interaction between the quantum bus and the probes, coherent averaging leads to a Heisenberg limited (HL) scaling for the QFI (QFI proportional to N 2 ). Importantly this HL scaling can be obtained while starting with a separable state. This provides an advantage as generally one needs to use entangled states to achieve this scaling. Another important aspect in coherent averaging is the possibility to obtain the HL scaling by performing a measurement on the quantum bus only. These results were obtained using perturbation theory in the regime of weak interactions. In this thesis we go one step further in the study of the coherent averaging protocol. We extend the formalism of perturbation theory to encompass the possibility of estimating any parameter, in the regimes of strong and weak interactions. To illustrate the validity of our results, we introduce two models as examples for a coherent averaging scheme. In these models both the quantum bus and all the probes are qubits. In the ZZXX model, the free Hamiltonians do not commute with the interaction Hamiltonians and we have to rely on numerics to find non-perturbative solutions .In the ZZZZ model the free evolution Hamiltonians commute with the interaction Hamiltonians and we can find the exact solution analytically. Perturbation theory shows that in the strong interaction regime and starting with a separable state, we can estimate the parameter of the free evolution of the probes with a HL scaling if the free Hamiltonians do not commute with the interaction Hamiltonians. This is confirmed by the non-perturbative numerical results for the ZZXX model. In the weak interaction regime we only obtain a standard quantum limit (SQL) scaling for the parameter of the free evolution of the probes (QFI proportional to N ). When one has only access to the quantum bus, we show that the HL scaling found using the perturbation theory does not necessarily survive outside the regime of validity of the perturbation. This is especially the case as N becomes large. It is shown by comparing the exact analytical result to the perturbative result with the ZZZZ model. The same behaviour is observed with the ZZXX model using the non-perturbative numerical results. In our second project we investigate the estimation of the depolarizing channel and the phase-flip channel under non-ideal conditions. It is known that using an ancilla can lead to an improvement of the channel QFI (QFI maximized over input states feeding the channel) even if we act with the identity on the ancilla. This method is known as channel extension. In all generality the maximal channel QFI can be obtained using an ancilla whose Hilbert space has the same dimension as the dimension of the Hilbert space of the original system. In this ideal scenario using multiple ancillas — or one ancilla with a larger Hilbert space dimension — is useless. To go beyond this ideal result we take into account the possibility of loosing either the probe or a finite number of ancillas. The input states considered are GHZ and W states with n + 1 qubits (the probe plus n ancillas). We show that for any channel, when the probe is lost then all the information is lost, and the use of ancillas cannot help. For the phase-flip channel the introduction of ancillas never improves the channel QFI and ancillas are useless. For the depolarizing channel the maximal channel QFI can be reached using one ancilla and feeding the extended channel with a Bell state, but if the ancilla is lost then all the advantage is lost. We show that the GHZ states do not help to fight the loss of ancillas: If one ancilla or more are lost all the advantage provided by the use of ancillas is lost. More interestingly, we show that the W states with more than one ancilla are robust against loss. For a given number of lost ancillas, there always exists an initial number of ancillas for which a W state provides a higher QFI than the one obtained without ancillas. Our last project is about Hamiltonian parameter estimation for arbitrary Hamiltonians. It is known that channel extension does not help for unitary channels. Instead we apply the idea of extension to the Hamiltonian itself and not to the channel. This is done by adding to the Hamiltonian an extra term, which is independent of the parameter and which possibly encompasses interactions with an ancilla. We call this technique Hamiltonian extension. We show that for arbitrary Hamiltonians there exists an upper bound to the channel QFI that is in general not saturated. This result is known in the context of non-linear metrology. Here we show explicitly the conditions to saturate the bound. We provide two methods for Hamiltonian extensions, called signal flooding and Hamiltonian subtraction, that allow one to saturate the upper bound for any Hamiltonian. We also introduce a third method which does not saturate the upper bound but provides the possibility to restore the quadratic time scaling in the channel QFI when the original Hamiltonian leads only to a periodic time scaling of the channel QFI. We finally show how these methods work using two different examples. We study the estimation of the strength of a magnetic field using a NV center, and show how using signal flooding we saturate the channel QFI. We also consider the estimation of a direction of a magnetic field using a spin-1. We show how using signal flooding or Hamiltonian subtraction we saturate the channel QFI. We also show how by adding an arbitrary magnetic field we restore the quadratic time scaling in the channel QFI. Eventually we explain how coherent averaging can be scrutinized in the formalism of Hamiltonian extensions

Magnetic resonance spectroscopy investigation in the right human hippocampus following spinal cord injury.

OBJECTIVE Preclinical studies have shown that cognitive impairments following spinal cord injury (SCI), such as impaired spatial memory, are linked to inflammation, neurodegeneration, and reduced neurogenesis in the right hippocampus. This cross-sectional study aims to characterize metabolic and macrostructural changes in the right hippocampus and their association to cognitive function in traumatic SCI patients. METHODS Within this cross-sectional study, cognitive function was assessed in 28 chronic traumatic SCI patients and 18 age-, sex-, and education-matched healthy controls by a visuospatial and verbal memory test. A magnetic resonance spectroscopy (MRS) and structural MRI protocol was performed in the right hippocampus of both groups to quantify metabolic concentrations and hippocampal volume, respectively. Group comparisons investigated changes between SCI patients and healthy controls and correlation analyses investigated their relationship to memory performance. RESULTS Memory performance was similar in SCI patients and healthy controls. The quality of the recorded MR spectra was excellent in comparison to the best-practice reports for the hippocampus. Metabolite concentrations and volume of the hippocampus measured based on MRS and MRI were not different between two groups. Memory performance in SCI patients and healthy controls was not correlated with metabolic or structural measures. CONCLUSION This study suggests that the hippocampus may not be pathologically affected at a functional, metabolic, and macrostructural level in chronic SCI. This points toward the absence of significant and clinically relevant trauma-induced neurodegeneration in the hippocampus

THEORETICAL ASPECTS AND REAL ISSUES IN AN INTEGRATED MULTIRADAR SYSTEM

In the last few years Homeland Security (HS) has gained a considerable interest in the research community. From a scientific point of view, it is a difficult task to provide a definition of this research area and to exactly draw up its boundaries. In fact, when we talk about the security and the surveillance, several problems and aspects must be considered. In particular, the following factors play a crucial role and define the complexity level of the considered application field: the number of potential threats can be high and uncertain; the threat detection and identification can be made more complicated by the use of camouflaging techniques; the monitored area is typically wide and it requires a large and heterogeneous sensor network; the surveillance operation is strongly related to the operational scenario, so that it is not possible to define a unique approach to solve the problem [1]. Information Technology (IT) can provide an important support to HS in preventing, detecting and early warning of threats. Even though the link between IT and HS is relatively recent, sensor integration and collaboration is a widely applied technique aimed to aggregate data from multiple sources, to yield timely information on potential threats and to improve the accuracy in monitoring events [2]. A large number of sensors have already been developed to support surveillance operations. Parallel to this technological effort in developing new powerful and dedicated sensors, interest in integrating a set of stand-alone sensors into an integrated multi-sensor system has been increasing. In fact, rather than to develop new sensors to achieve more accurate tracking and surveillance systems, it is more useful to integrate existing stand-alone sensors into a single system in order to obtain performance improvements In this dissertation, a notional integrated multi-sensor system acting in a maritime border control scenario for HS is considered. In general, a border surveillance system is composed of multiple land based and moving platforms carrying different types of sensors [1]. In a typical scenario, described in [1], the integrated system is composed of a land based platform, located on the coast, and an airborne platform moving in front of the coast line. In this dissertation, we handle two different fundamental aspects. In Part I, we focus on a single sensor in the system, i.e. the airborne radar. We analyze the tracking performance of such a kind of sensor in the presence of two different atmospheric problems: the turbulence (in Chapter 1) and the tropospheric refraction (in Chapter 2). In particular, in Chapter 1, the losses in tracking accuracy of a turbulence-ignorant tracking filter (i.e. a filter that does not take into account the effects of the atmospheric turbulences) acting in a turbulent scenario, is quantified. In Chapter 2, we focus our attention on the tropospheric propagation effects on the radar electromagnetic (em) signals and their correction for airborne radar tracking. It is well known that the troposphere is characterized by a refractive index that varies with the altitude and with the local weather. This variability of the refractive index causes an error in the radar measurements. First, a mathematical model to describe and calculate the em radar signal ray path in the troposphere is discussed. Using this mathematical model, the errors due to the tropospheric propagation are evaluated and the corrupted radar measurements are then numerically generated. Second, a tracking algorithm, based on the Kalman Filter, that is able to mitigate the tropospheric errors during the tracking procedure, is proposed. In Part II, we consider the integrated system in its wholeness to investigate a fundamental prerequisite of any data fusion process: the sensor registration process. The problem of sensor registration (also termed, for naval system, the grid-locking problem) arises when a set of data coming from two or more sensors must be combined. This problem involves a coordinate transformation and the reciprocal alignment among the various sensors: streams of data from different sensors must be converted into a common coordinate system (or frame) and aligned before they could be used in a tracking or surveillance system. If not corrected, registration errors can seriously degrade the global system performance by increasing tracking errors and even introducing ghost tracks. A first basic distinction is usually made between relative grid-locking and absolute grid-locking. The relative grid-locking process aligns remote data to local data under the assumption that the local data are bias free and that all biases reside with the remote sensor. The problem is that, actually, also the local sensor is affected by bias. Chapter 3 of this dissertation is dedicated to the solution of the relative grid-locking problem. Two different estimation algorithms are proposed: a linear Least Squares (LS) algorithm and an Expectation-Maximization-based (EM) algorithm. The linear LS algorithm is a simple and fast algorithm, but numerical results have shown that the LS estimator is not efficient for most of the registration bias errors. Such non-efficiency could be caused by the linearization implied by the linear LS algorithm. Then, in order to obtain a more efficient estimation algorithm, an Expectation-Maximization algorithm is derived. In Chapter 4 we generalize our findings to the absolute grid-locking problem. Part III of this dissertation is devoted to a more theoretical aspect of fundamental importance in a lot of practical applications: the estimate of the disturbance covariance matrix. Due to its relevance, in literature it can be found a huge quantity of works on this topic. Recently, a new geometrical concept has been applied to this estimation problem: the Riemann (or intrinsic) geometry. In Chapter 5, we give an overview on the state of the art of the application of the Riemann geometry for the covariance matrix estimation in radar problems. Particular attention is given for the detection problem in additive clutter. Some covariance matrix estimators and a new decision rule based on the Riemann geometry are analyzed and their performance are compared with the classical ones. [1] Sofia Giompapa, “Analysis, modeling, and simulation of an integrated multi-sensor system for maritime border control”, PhD dissertation, University of Pisa, April 2008. [2] H. Chen, F. Y. Wang, and D. Zeng, “Intelligence and security informatics for Homeland Security: information, communication and transportation,” Intelligent Transportation Systems, IEEE Transactions on, vol. 5, no. 4, pp. 329-341, December 2004

On the recursive joint position and attitude determination in multi-antenna GNSS platforms

Global Navigation Satellite Systems’ (GNSS) carrier phase observations are fundamental in the provision of precise navigation for modern applications in intelligent transport systems. Differential precise positioning requires the use of a base station nearby the vehicle location, while attitude determination requires the vehicle to be equipped with a setup of multiple GNSS antennas. In the GNSS context, positioning and attitude determination have been traditionally tackled in a separate manner, thus losing valuable correlated information, and for the latter only in batch form. The main goal of this contribution is to shed some light on the recursive joint estimation of position and attitude in multi-antenna GNSS platforms. We propose a new formulation for the joint positioning and attitude (JPA) determination using quaternion rotations. A Bayesian recursive formulation for JPA is proposed, for which we derive a Kalman filter-like solution. To support the discussion and assess the performance of the new JPA, the proposed methodology is compared to standard approaches with actual data collected from a dynamic scenario under the influence of severe multipath effects