Multiparameter squeezing for optimal quantum enhancements in sensor networks

Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.Comment: 8 + 10 pages, 4 + 1 figure

Precision of Parameter Estimation in Quantum Metrology

The fundamental precision limit of an interferometer is crucial since it bounds the best possible sensitivity one could achieve using such a device. This thesis will focus on several different interferometers and try to give the ultimate precision bounds by carefully counting all the resources used in the interferometers. The thesis begins with the basics of the quantum state of light. The fundamentals of quantum metrology are also reviewed and discussed. More specifically, the terminology of classical and quantum Cram\\u27er-Rao bound and classical and quantum Fisher information are introduced. Chapter 3 discusses the conclusive precision bounds in two-mode interferometer such as Mach-Zehnder interferometer (MZI) and SU(1,1) interferometer. I revisit the quantum Fisher information approach of these two interferometers and show the discrepancy of phase sensitivity on the physically same setup. Then I establish fundamental precision estimation bounds for such device, due to the reason that many works of literature fail to accurately count the resources and knowledge of phase-to-be-estimated used in the interferometers. The analysis suggests that for a MZI, one can never do better than SNL in phase sensitivity, when an input to one of the two ports is the vacuum. If one does not allow the detector to use any external phase reference or power resource, then the precision is limited by the SNL. For a SU(1,1) interferometer, firstly, when one of the input states is restricted to be a vacuum state, I showed that by using either the phase-averaging method or the quantum Fisher information matrix method, different phase configurations of the SU(1,1) interferometer result in the same QFI. Secondly, I compared the results of the phase-averaging method and the quantum Fisher information matrix method, and then I argued that for an SU(1,1) interferometer, phase averaging or quantum Fisher information matrix method is generally required, and they are equivalent. Finally, I used the quantum Fisher information matrix method to calculate the precision limit for other common input states, such as two coherent state inputs or coherent state with squeezed vacuum inputs. In chapter 4, I will consider a passive multi-mode interferometer for multiparameter phase estimation. It was suggested that optical networks with relatively inexpensive overhead---single photon Fock states, passive optical elements, and single photon detection---can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small. In this chapter, I analytically compute the quantum Cramer-Rao bound to show these networks can have a constant-factor quantum advantage in multi-parameter estimation for even large number of modes. Additionally, I provide a simplified measurement scheme using an array of single photon detectors and only one number-resolving detector that is capable of approximately obtaining this sensitivity for a small number of modes. Remarkably, supersensitivity can be observed even with inefficient but heralded single photon sources

Structural Susceptibility and Separation of Time Scales in the van der Pol Oscillator

We use an extension of the van der Pol oscillator as an example of a system with multiple time scales to study the susceptibility of its trajectory to polynomial perturbations in the dynamics. A striking feature of many nonlinear, multi-parameter models is an apparently inherent insensitivity to large magnitude variations in certain linear combinations of parameters. This phenomenon of "sloppiness" is quantified by calculating the eigenvalues of the Hessian matrix of the least-squares cost function which typically span many orders of magnitude. The van der Pol system is no exception: Perturbations in its dynamics show that most directions in parameter space weakly affect the limit cycle, whereas only a few directions are stiff. With this study we show that separating the time scales in the van der Pol system leads to a further separation of eigenvalues. Parameter combinations which perturb the slow manifold are stiffer and those which solely affect the transients in the dynamics are sloppier.Comment: 7 pages, 4 figure

Research in computer technology, spectrometry, control systems, vacuum instrumentation, plasma physics, superconductivity and related topics Progress report, Jun. - Aug. 1965

Research projects on surface and plasma physics, computer programming, information processing, superconductivity, ionospheric data, network synthesis and related field

The Role of Auxiliary Stages in Gaussian Quantum Metrology

The optimization of the passive and linear networks employed in quantum metrology, the field that studies and devises quantum estimation strategies to overcome the levels of precision achievable via classical means, appears to be an essential step in certain metrological protocols achieving the ultimate Heisenberg-scaling sensitivity. This optimization is generally performed by adding degrees of freedom by means of auxiliary stages, to optimize the probe before or after the interferometric evolution, and the choice of these stages ultimately determines the possibility to achieve a quantum enhancement. In this work we review the role of the auxiliary stages and of the extra degrees of freedom in estimation schemes, achieving the ultimate Heisenberg limit, which employ a squeezed-vacuum state and homodyne detection. We see that, after the optimization for the quantum enhancement has been performed, the extra degrees of freedom have a minor impact on the precision achieved by the setup, which remains essentially unaffected for networks with a larger number of channels. These degrees of freedom can thus be employed to manipulate how the information about the structure of the network is encoded into the probe, allowing us to perform quantum-enhanced estimations of linear and non-linear functions of independent parameters

[Research Pertaining to Physics, Space Sciences, Computer Systems, Information Processing, and Control Systems]

Research project reports pertaining to physics, space sciences, computer systems, information processing, and control system

ALL RIGHTS RESERVEDSCIENCE IN HIGH DIMENSIONS: MULTIPARAMETER MODELS AND BIG DATA

Complex multiparameter models such as in climate science, economics, systems biology, materials science, neural networks and machine learning have a large-dimensional space of undetermined parameters as well as a large-dimensional space of predicted data. These high-dimensional spaces of inputs and outputs pose many challenges. Recent work with a diversity of nonlinear predictive models, microscopic models in physics, and analysis of large datasets, has led to important insights. In particular, it was shown that nonlinear fits to data in a variety of multiparameter models largely rely on only a few stiff directions in parameter space. Chapter 2 explores a qualitative basis for this compression of parameter space using a model nonlinear system with two time scales. A systematic separation of scales is shown to correspond to an increasing insensitivity of parameter space directions that only affect the fast dynamics. Chapter 3 shows with the help of microscopic physics models that emergent theories in physics also rely on a sloppy compression of the parameter space where macroscopically relevant variables form the stiff directions. Lastly, in chapter 4, we will learn that the data space of historical daily stock returns of US public companies has an emergent simplex structure that makes it amenable to a low-dimensional representation. This leads t