It can be said that all of humanity's efforts can be understood as a problem of optimization. We each have a natural sense of what is ``good'' or ``bad'' and thus our actions tend towards maximizing -- or optimizing -- some notion of good and minimizing those things we perceive as bad or undesirable. Within the sciences, the greatest form of good is knowledge. It is this pursuit of knowledge that leads to not only life-saving innovations and technology, but also to furthering our understanding of our natural world and driving our philosophical pursuits. The principle method of obtaining knowledge in the sciences is by performing measurements; the simple act of comparing one attribute of a system to a known standard and recording the observed value is how all scientific progress is made. The act of performing measurements is in fact so important that there is an entire field of study surrounding it: metrology. One critical component of metrology is the development of new techniques to perform measurements, or alternative measurement schemes that are more optimal in some way. This is where there is room to exploit quantum physics to improve our techniques \--- we can perform quantum metrology. In quantum mechanics we routinely deal with the smallest, weakest, most delicate of systems. Quantum properties are inherently very sensitive to their environment; this of course makes them highly intolerant of noise but also makes them great resources to perform sensitive measurements. Quantum metrology concerns itself with utilizing quantum phenomena to extract more information from the natural world than is possible by conventional, or classical, means. To perform optimal measurements, these quantum systems must of course be optimal by some metric. Performing the ``optimal'' measurement requires several ingredients. First, we need the optimal tools or instrumentation. In quantum mechanical language, this means we need the optimal probe state. Then, we need to optimize the interaction of our instrumentation with the system we which to interrogate so that we can extract the desired information. This translates to needing the best possible interaction between the probe state and the system in question -- in other words, we need to optimize the evolution of the probe. Finally, we must take care to extract the most information as possible at the output; we must not neglect any information present in the evolved probe state. The entire quantum metrology process can be summarized as thus: probe
It can be said that all of humanity's efforts can be understood as a problem of optimization. We each have a natural sense of what is good'' or bad'' and thus our actions tend towards maximizing -- or optimizing -- some notion of good and minimizing those things we perceive as bad or undesirable. Within the sciences, the greatest form of good is knowledge. It is this pursuit of knowledge that leads to not only life-saving innovations and technology, but also to furthering our understanding of our natural world and driving our philosophical pursuits. The principle method of obtaining knowledge in the sciences is by performing measurements; the simple act of comparing one attribute of a system to a known standard and recording the observed value is how all scientific progress is made. The act of performing measurements is in fact so important that there is an entire field of study surrounding it: metrology. One critical component of metrology is the development of new techniques to perform measurements, or alternative measurement schemes that are more optimal in some way. This is where there is room to exploit quantum physics to improve our techniques --- we can perform quantum metrology. In quantum mechanics we routinely deal with the smallest, weakest, most delicate of systems. Quantum properties are inherently very sensitive to their environment; this of course makes them highly intolerant of noise but also makes them great resources to perform sensitive measurements. Quantum metrology concerns itself with utilizing quantum phenomena to extract more information from the natural world than is possible by conventional, or classical, means. To perform optimal measurements, these quantum systems must of course be optimal by some metric. Performing the ``optimal'' measurement requires several ingredients. First, we need the optimal tools or instrumentation. In quantum mechanical language, this means we need the optimal probe state. Then, we need to optimize the interaction of our instrumentation with the system we which to interrogate so that we can extract the desired information. This translates to needing the best possible interaction between the probe state and the system in question -- in other words, we need to optimize the evolution of the probe. Finally, we must take care to extract the most information as possible at the output; we must not neglect any information present in the evolved probe state. The entire quantum metrology process can be summarized as thus: probe
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.
Quantum mechanics has profoundly reshaped our knowledge of the physical world: a deep comprehension of the quantum nature of matter yielded to the so-called first quantum revolution, enabling transformative technologies ranging from lasers to semiconductor de- vices, being at the heart of the digital revolution characterizing the second half of the XXth century. Furthermore, the capability of manipulating and controlling individual quantum systems enabled a totally different working paradigm, obeying the logic im- posed by quantum physics, paving the way, at the end of the XXth and the beginning of the XXIst century, for the second quantum revolution. Modern quantum technologies, including quantum computation, quantum simulation, quantum metrology and quantum communication rely on peculiar quantum phenomena, such as superposition, entangle- ment and coherence to perform tasks beyond classical capabilities. This thesis proposes quantum metrology as a unifying conceptual and methodological framework to investigate problems lying at the intersection of fundamental quantum physics and quantum information science. More in detail, it addresses theoretical and experimental protocols to certify the presence of quantum correlations (namely, quantum steering), as well as to design secure sensing in quantum networks under realistic assump- tions. Moreover, it also suggest how tunable-strength measurement-based strategies can be used to extract information from complex systems even in seemingly inaccessible sce- narios. Overall, this thesis proposes quantum metrology as a framework through which the purest nature of information can be probed, certified and secured at the most fundamental level.
The foundational theory of quantum enhanced metrology for parameter estimation is of fundamental importance to the progression of science and technology as the scientific method is built upon empirical evidence, the acquisition of which is entirely reliant on measurement. Quantum mechanical properties can be exploited to yield measurement results to a greater precision (lesser uncertainty) than that which is permitted by classical methods. This has been mathematically demonstrated by the derivation of theoretical bounds which place a fundamental limit on the uncertainty of a measurement. Furthermore, quantum metrology is of immediate interest in the application of quantum technologies since measurement plays a central role. This thesis focuses on the role of quantum correlations and uncertainty relations which govern the precision bounds. We show how correlations can be distributed amongst limited resources in realistic scenarios, as permitted by current experimental capabilities, to achieve higher precision measurements than current approaches. This is extended to the setting of multiparameter estimation in which we demonstrate a more technologically feasible method of correlation distribution than those previously posited which perform as well as, or worse than, our scheme. Furthermore, a quantum metrology protocol is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. We consider the more realistic sensing scenario of time being a limited resource which is divided amongst the three stages and demonstrate the most efficient use of this resource. Additionally, we take an information theoretic approach to quantum mechanical uncertainty relations and derive a one-parameter class of uncertainty relations which supplies more information about the quantum mechanical system of interest than conventional uncertainty relations. Finally, we demonstrate how we can use this class of uncertainty relations to reconstruct information of the state of the quantum mechanical system.
The insights offered by quantum mechanics to the field of optical metrology are many-fold, with non-classical states of light themselves used to make sensors that surpass the sensitivity of sensors using classical states of light. Unfortunately, this advantage, referred to often as "super-sensitivity" is notoriously fragile, and even the slightest experimental imperfections may greatly reduce the efficacy of the non-classical sensors, sometimes completely obviating their advantage. In my thesis I have shown that the performance of an otherwise ideal two-photon interferometer, which exploits entanglement between photons to make super-sensitive measurements of phase, is crippled by the slightest introduction of decoherence between modes of the interferometer. I have shown further that such drastic reduction in sensitivity can also appear in classical measurement problems, specifically that the recently developed methods of estimating the separation between a pair of point sources are rendered less effective when the ideal assumption of complete spatial incoherence is relaxed. Towards overcoming these and other issues, I have designed new configurations that use ancillary optical degrees of freedom, a tool-set that has recently garnered much interest in the field of quantum optics. In the context of two-photon interferometry, I have shown that by coupling polarization to the spatial-structure of the two photon state used to probe phase it is possible to obviate the need for a reference phase, even in the context of decoherence and imperfections in the interferometer. In the context of two-point resolution, I have developed an anisotropic imaging system that performs the function of an image-inversion interferometer and is inherently stable, offering an attractive implementation of recently developed methods of sub-Rayleigh imaging. I have further shown both theoretically and experimentally that the same anisotropic image-inversion interferometer is useful in measuring spatially encoded phases, both in the context of classical illumination as well as quantum-aided two-photon super-sensing. In both cases, the ability to perform interferometric measurements of the spatial structure of an electric field without splitting beam paths forms a bridge between conception and implementation of precision-sensing measurement strategies. Finally, I have shown that binary interferometric method based on the common-path anisotropic imaging system that I introduced, are able to measure both phase gradients and transverse beam tilts with a sensitivity beating conventional systems that are used both commercially and in research laboratories.
In 2009, physicists at the National Institute of Standards and Technology in Colorado, Boulder developed what could arguable be called the first rudimentary quantum computer [1]. The past decade has seen unprecedented improvements in quantum information science culminating in the demonstration of quantum supremacy --- that quantum computers can solve problems that are impractical to be solved on the best supercomputers [2]. This remarkable progress necessitates the development of techniques to characterize the quantum devices that are being developed. In my thesis, I will focus on such devices that manipulate and detect light. In Chapter 1, I will introduce the reader to the historical underpinnings of the study of light. After surveying the history of light since time immemorial, I will delve into the developments in the study of light in the 19th and the early 20th century. I will then present a brief introduction to quantum mechanics. I end this chapter by demonstrating how light is quantized. In Chapter 2, I will introduce the various tools necessary to delve into this dissertation. After defining quadrature operators and Wigner functions, I will introduce various states of light used in this thesis. I will then discuss how the evolution, as well as detection of quantum optical states, are modelled. I will then present the formalism of Gaussian quantum information that simplifies the manipulation of certain states of light. Finally, I will briefly talk about quantum metrology and show its advantage in phase estimation. In Chapter 3, I will introduce a method to characterize linear and quadratically nonlinear optical systems. After motivating the need for this work, I will introduce the modifications necessary to the standard Mach-Zehnder interferometer in order to characterize optical systems with it. I will then show how to characterize linear optical systems with coherent probes. I will also show that this scheme is shot-noise limited. I will then show that by using single photons in addition, we can characterize quadratically nonlinear optical systems. Finally, I will show that no advantage is gained in sensitivity by using squeezed light along with coherent light as probes. In Chapter 4, I will introduce a method to characterize photodetectors. This is done by developing an experimental method to find the Wigner functions of the POVM set corresponding to a photodetector. After motivating the necessity of this work as well as describing the proposed experimental setup, I will show how this scheme can
Quantum theory is one of the most successful theories that have influenced the course of
scientific progress during the twentieth century. It has presented a new line of scientific thought, predicted entirely inconceivable situations and influenced several domains of
modern technologies. There are many different ways for expressing laws of science in
general and laws of physics in particular. Similar to physical laws of nature, information
can also be expressed in different ways. The fact that information can be expressed in
different ways without losing its essential nature, leads for the possibility of the automatic
manipulation of information.
Quantum computing is a study area that focuses on developing computers based on the properties of “quantum theory” & “quantum physics”. Quantum theory defines the behavior & nature of energy and matter on the “atomic” and “subatomic” levels also known as the quantum levels. A quantum computer is a computational device that utilizes the phenomena of quantum mechanics with its quantum properties to structure & process data. A large-scale quantum computer is capable of performing operations in exponentially enormous speed compared to a classical computer. Development of such computers is considered a massive leap for mankind in computing abilities with huge performance gains for simulations or brute force for example.
All ways of expressing information use physical system, spoken words are
conveyed by air pressure fluctuations: “No information without physical representation”.
Quantum computers are not meant to replace typical computers. In practice, they will be separate instruments used to solve complex, data-heavy problems, particularly those that make use of machine learning, where the system can make predictions and improve over time.