Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

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Mathematical Methods Of Statistics

It is well known that the photon is only a quanta of electromagnetic radiation However, there are many myths around the photon in contemporary physics, for example, the photon loses energy when traveling through space The article explains the basic features of the photon, such as wave-particle duality, the relation between a continuous electromagnetic wave and a quanta, the interaction of electric and magnetic fields, space of photon, speed of light

Nature of Photon

September 19-20 International Student Orientation September 22 New Student check-In for Undergraduates September 22-29 New Student Orientation for Undergraduates September 23 New Student Check-In for Graduates September 23-27 New Student Orientation for Graduates September 26 Undergraduate Academic Standards and Honors Committee – 1:00 p.m. September 27 Undergraduate Academic Standards and Honors Committee Appeals– 1:00 p.m. September 30 Rosh Hashanah – classes excused October 1 Beginning of instruction 8:00 a.m. October 18 Last day for adding courses and removing conditions and incompletes October 30Midterm examination period November 5 November 11 Midterm deficiency notices due 9:00 a.m. November 20 Last day for dropping courses, exercising pass/fail option, and changing sections November 21Registration for winter term 2019-20 December 6 November 28-29 Thanksgiving (Institute holiday) December 6 Last day of classes Last day to register for winter term 2019-20 without a $50 late fee December 7-10 Study period December 11*-13 Final examinations, fall term 2019-20 December 13 End of fall term 2019-20 December 14Winter recess January 5 December 18 Instructors' final grade reports due 9:00 a.m. *First due date for final examinations

カリフォルニア工科大学 (California Institute of technology) 滞在記

Information geometry is a new mathematical discipline which applies the methodology of differential geometry to statistics. Therefore, families of exponential distributions are considered as embedded manifolds, called statistical manifolds. This includes so important families like the multivariate normal or the gamma distributions. Fisher information — well known in information theory — becomes a metric on statistical manifolds. The Fisher information metric enables a hyperbolic structure on the multivariate normal distributions. Information geometry offers new methods for hypothesis testings, estimation theory or stochastic filtering. These can be used in engineering areas like signal processing or video processing or finance.

http://ieeexplore.ieee.org/iel5/6423297/6450609/06450636.pdf

Information geometry and its applications

Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, we collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. We give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. We address the question how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.

/pdf/a-geometric-perspective-on-quantum-parameter-estimation-1x1yj9481j.pdf

A Geometric Perspective on Quantum Parameter Estimation

Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this Review, the authors collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. The authors give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. The authors address the question of how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this Review, the authors collect some of the key theoretical results in quantum parameter estimation by presenting the theory for the quantum estimation of a single parameter, multiple parameters, and optical estimation using Gaussian states. The authors give an overview of results in areas of current research interest, such as Bayesian quantum estimation, noisy quantum metrology, and distributed quantum sensing. The authors address the question of how minimum measurement errors can be achieved using entanglement as well as more general quantum states. This review is presented from a geometric perspective. This has the advantage that it unifies a wide variety of estimation procedures and strategies, thus providing a more intuitive big picture of quantum parameter estimation.

/pdf/geometric-perspective-on-quantum-parameter-estimation-2he89dngy1.pdf

Geometric perspective on quantum parameter estimation

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has greatly diminished the applicability of estimation theory in many practical implementations. The Holevo Cramer-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multi-parameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimisation over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing, and characterise the performance of state tomography on the codespace of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial codestates can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress towards the estimation of multiple incompatible observables.

Tight bounds on the simultaneous estimation of incompatible parameters

Concerted efforts are underway to establish an infrastructure for a global quantum internet to realise a spectrum of quantum technologies. This will enable more precise sensors, secure communications, and faster data processing. Quantum communications are a front-runner with quantum networks already implemented in several metropolitan areas. A number of recent proposals have modelled the use of space segments to overcome range limitations of purely terrestrial networks. Rapid progress in the design of quantum devices have enabled their deployment in space for in-orbit demonstrations. We review developments in this emerging area of space-based quantum technologies and provide a roadmap of key milestones towards a complete, global quantum networked landscape. Small satellites hold increasing promise to provide a cost effective coverage required to realised the quantum internet. We review the state of art in small satellite missions and collate the most current in-field demonstrations of quantum cryptography. We summarise important challenges in space quantum technologies that must be overcome and recent efforts to mitigate their effects. A perspective on future developments that would improve the performance of space quantum communications is included. We conclude with a discussion on fundamental physics experiments that could take advantage of a global, space-based quantum network.

Advances in Space Quantum Communications

We introduce spatial deformations to an array of light sources and study how the estimation precision of the interspacing distance $d$ changes with the sources of light used. The quantum Fisher information (QFI) is used as the figure of merit in this work to quantify the amount of information we have on the estimation parameter. We derive the generator of translations $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathcal{G}}$ in $d$ due to an arbitrary homogeneous deformation applied to the array. We show how the variance of the generator can be used to easily consider how different deformations and light sources can effect the estimation precision. The single-parameter estimation problem is applied to the array, and we report on the optimal state that maximizes the QFI for $d$. Contrary to what may have been expected, the higher average mode occupancies of the classical states performs better in estimating $d$ when compared with single photon emitters (SPEs). The optimal entangled state is constructed from the eigenvectors of the generator and found to outperform all these states. We also find the existence of multiple optimal estimators for the measurement of $d$. Our results find applications in evaluating stresses and strains, fracture prevention in materials expressing great sensitivities to deformations, and selecting frequency distinguished quantum sources from an array of reference sources.

/pdf/quantum-metrology-of-spatial-deformation-using-arrays-of-2n18ahc4wl.pdf

Jasminder S. Sidhu

Papers

A Geometric Perspective on Quantum Parameter Estimation

Geometric perspective on quantum parameter estimation

Tight bounds on the simultaneous estimation of incompatible parameters

Advances in Space Quantum Communications

Quantum metrology of spatial deformation using arrays of classical and quantum light emitters