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Resources in quantum imaging, detection and estimation

Sammy Ragy

Published Jul 15, 2015• 1 citation
OpenAlex

Abstract

The research included in this thesis comes in two main bodies. In the first, the focus is on intensity interferometric schemes, and I attempt to identify the types of correlations dominant in their operation. This starts with the, now rather historical, Hanbury Brown and Twiss setup from the 1950s and progresses to more recent interests such as ghost imaging and a variant of `quantum illumination', which is a quantum-enhanced detection scheme. These schemes are considered in the continuous variable regime, with Gaussian states in particular. Intensity interferometry has been the cause of a number of disputes between quantum opticians over the past 60 years and I weigh in on the arguments using relatively recent techniques from quantum information theory. In the second half, the focus turns away from the optical imaging and detection schemes, and onto quantum estimation -- multiparameter quantum estimation to be precise. This is an intriguing area of study where one has to carefully juggle tradeoffs in choosing both the optimal measurement and optimal state for performing an estimation in two or more parameters. I lay out a framework for circumventing some of the difficulties involved in this and apply it to several physical examples, revealing some interesting and at times counterintuitive features of multiparameter estimation.

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The research included in this thesis comes in two main bodies. In the first, the focus is on intensity interferometric schemes, and I attempt to identify the types of correlations dominant in their operation. This starts with the, now rather historical, Hanbury Brown and Twiss setup from the 1950s and progresses to more recent interests such as ghost imaging and a variant of `quantum illumination', which is a quantum-enhanced detection scheme. These schemes are considered in the continuous variable regime, with Gaussian states in particular. Intensity interferometry has been the cause of a number of disputes between quantum opticians over the past 60 years and I weigh in on the arguments using relatively recent techniques from quantum information theory. In the second half, the focus turns away from the optical imaging and detection schemes, and onto quantum estimation -- multiparameter quantum estimation to be precise. This is an intriguing area of study where one has to carefully juggle tradeoffs in choosing both the optimal measurement and optimal state for performing an estimation in two or more parameters. I lay out a framework for circumventing some of the difficulties involved in this and apply it to several physical examples, revealing some interesting and at times counterintuitive features of multiparameter estimation.
We compare the performance of quantum imaging schemes based on spatially correlated photon pairs by formulating them as quantum multiparameter estimation problems, in which the object is characterized by transmission coefficients associated with different spatial modes. Our work focuses on standard quantum imaging techniques such as ghost imaging, two-photon imaging, and imaging with undetected photons. Specifically, we compute the quantum Fisher information matrices and show that they are saturated by Fisher information matrices corresponding to measurements in the object-mode basis, which generalize the common detection schemes employed in each imaging configuration. We find that ghost imaging and two-photon imaging generally provide higher precision for transmission estimation than imaging with undetected photons, but the latter is the only one that naturally does not couple transmission estimation across different spatial modes. These results identify which imaging protocols are best suited for specific tasks and provide practical guidelines for the design and optimization of quantum sensing technologies based on spatial correlations.
We present a review on quantum metrology and sensing, from its foundations to current applications. Highlights of the review include consideration of both frequentist and Bayesian approaches to parameter estimation; single as well as multiparameter estimation; estimation for different encoding processes comprising unitary as well as noisy channels, quantum thermometry, and channels involving indefinite causal order; different estimation strategies incorporating also recent advances like quantum error correction-aided methods and reservoir engineering; usefulness of quantum Fisher information to detect resources; applications of quantum metrology in diverse arenas covering quantum many-body sensors, sensing protocols in atomic ensembles, atom-photon systems, and continuous-variable systems, quantum imaging, quantum illumination, atomic clocks and atom interferometry, etc; and experimental realizations of quantum sensors in different physical platforms.
In this thesis I examine how the statistical properties of radiation limit our ability to perform imaging and metrological procedures. In particular I focus on radiation in the far field zone of the source. The classical and quantum theories of parameter estimation are introduced and subsequently utilised throughout, along with the theory of optical coherence. Classical and quantum imaging protocols are examined with the aid of a resolution criterion and the criterion is shown to reproduce the results of previous works. This method is also extended to previously un-investigated situations and the effect of imperfect measurements is explored. Intensity correlation measurements are investigated in great detail and for the first time a rigorous comparison is made between higher-order intensity correlation measurements of the type introduced by Hanbury Brown and Twiss. The importance of considering covariances in intensity correlation data is demonstrated and I give a full, detailed account of how to include this in the formulation. I also show how the optimal arrangement for an intensity correlation measurement can be found, therefore allowing the best precision in parameter estimation to be achieved. A quantum mechanical description of blackbody radiation is used to examine the state arriving at a detector in the far field. By using the quantum Fisher information an interesting connection is found between the statistical independence of photons in the source plane and the acquisition of information in the far field.
The concepts of quantum detection and estimation theory can be of great help in the analysis of faint signals, which must be treated with extreme care due to the fragility and subtlety. But this is surely not the only domain, where the advanced concepts may be applied. Strong optical fields can be analyzed by similar techniques since by virtue of first quantization any optical wave plays role of a quantum state. More precisely, a classical mode of light can be given and alternative interpretation as a quantum state of the spatial degrees of freedom of a photon. Here the formulation of classical optics meets those of quantum information processing. The goal of the research is to optimize classical sensing schemes of strong signals in order to attain the best performance allowed by Nature. As examples of the approach, measurement of two point-like sources separation and full characterization of laser beams by a phase-space tomography will be discussed both theoretically and experimentally.
Recent years have witnessed a growing interest in understating the limitations imposed by quantum noise in precision measurements and devising techniques to reduce it. The attention is currently turning to the simultaneously estimation of several parameters of interest, driven by its promising potential across a wide range of sensing applications as well as fueled by experimental progress in various optical and atomic platforms. Here, we provide a comprehensive overview of key research directions in multiparameter quantum sensing and metrology, highlighting both opportunities and challenges. We introduce the basic framework, discuss ultimate sensitivity bounds, optimal measurement strategies, and the role of quantum incompatibility, showing important differences with respect to single-parameter estimation. Additionally, we discuss emerging experimental implementations in distributed quantum sensing, including cutting-edge optimization techniques. This review aims to bridge the gap between theory and experiments, paving the way for the next-generation of quantum sensors and their integration with other quantum technologies.
In this dissertation we begin with a brief introduction to quantum optics concentrating on the topics of the noise of quantum optical states, quantum estimation theory, quantum interferometry and the atom-field interaction. This background is necessary for understanding the discussions in later chapters. In particular, quantum interferometry, which is optical interferometry when the light source is a quantum mechanical state, plays a central role in this dissertation. In Chapter 2 we discuss the phase estimation sensitivity of quantum metrology when photon loss is present. In Chapter 3 we extend the discussion to include the phase fluctuation of the system caused by the environment. We model our metrological system with the Mach-Zehnder interferometer (MZI) and use a light field in the symmetric number-path entangled state as the source. In both chapters we use the parity operator as the detection scheme and show that it is optimal under pure dephasing. In Chapter 4 we discuss the application of quantum optical states in remote sensing and propose a new scheme for a quantum radar. Again, our scheme consists of a MZI and a coherent light source. It is shown that using only coherent states of light and quantum homodyne detection, super-resolving ranging and angle determination are achievable. Chapter 5 is devoted to the generation of a super-resolving single-photon number-path entangled state which may serve as a proof-of-principle prototype for quantum lithography. The repeated implementation of MZIs is shown to be able to remove photons coherently from both modes of a symmetric number-path entangled state with arbitrarily high photon number. Lastly, in Chapter 6 we introduce the phenomenon known as polarization self-rotation and discuss its potential in generating a squeezed vacuum state, which has a huge impact in quantum interferometry.