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Lectures on Quantum State Estimation
This is the 7th book in the author's 'Lectures on ...' book series, and the first aimed at graduate-level readers (two additional graduate texts are in preparation). Primarily intended for physics graduate students, the book is accessible to advanced undergraduates and will appeal to students with a background in statistics and a keen interest in quantum physics. By the end of this book, readers will be well-prepared for working on research projects that require the drawing of inference from the noisy data collected in quantum experiments, as epitomized by quantum state estimation.
The book begins with chapters on the basics of estimation theory and the basics of quantum theory. This includes, in particular, the roles played by the frequentist methods of statistics, which are crucial when planning an experiment, and the Bayesian methods, which are the tools for drawing inference from the actual data gathered. A central concept is that of optimal error regions that supplement the point estimators ('best guesses') with the analogs of error bars in the high-dimensional parameter space; there is, in particular, the plausible region which comprises all point estimators supported by the data.
Practical applications require the evaluation of high-dimensional integrals with the aid of Monte Carlo integration. For that, one needs to draw samples of quantum states from the relevant distributions, namely the priors and posteriors of Bayesian methodology. The book discusses the algorithms well-suited for this kind of sampling, which is central to the processing of real-life data.
The book illustrates all concepts with pertinent examples and offers numerous exerciseswhich the readers can practice and perfect their skills with. The presentation is detailed and does not skip technical steps, which makes the book particularly valuable for self-studying readers and as textbook adopted by lecturers teaching courses on this or related topics. While the book is based on lecture notes developed for the author's courses on quantum state estimation at NUS and BIT, this book also offers a comprehensive account of the concepts and methods developed in the author's group at CQT and presents this material in textbook form for the first time.
Researchers, students, university teachers, Statisticians with an interest in physics applications.
The book begins with chapters on the basics of estimation theory and the basics of quantum theory. This includes, in particular, the roles played by the frequentist methods of statistics, which are crucial when planning an experiment, and the Bayesian methods, which are the tools for drawing inference from the actual data gathered. A central concept is that of optimal error regions that supplement the point estimators ('best guesses') with the analogs of error bars in the high-dimensional parameter space; there is, in particular, the plausible region which comprises all point estimators supported by the data.
Practical applications require the evaluation of high-dimensional integrals with the aid of Monte Carlo integration. For that, one needs to draw samples of quantum states from the relevant distributions, namely the priors and posteriors of Bayesian methodology. The book discusses the algorithms well-suited for this kind of sampling, which is central to the processing of real-life data.
The book illustrates all concepts with pertinent examples and offers numerous exerciseswhich the readers can practice and perfect their skills with. The presentation is detailed and does not skip technical steps, which makes the book particularly valuable for self-studying readers and as textbook adopted by lecturers teaching courses on this or related topics. While the book is based on lecture notes developed for the author's courses on quantum state estimation at NUS and BIT, this book also offers a comprehensive account of the concepts and methods developed in the author's group at CQT and presents this material in textbook form for the first time.
Researchers, students, university teachers, Statisticians with an interest in physics applications.
355 pages, Kindle Edition
Published October 22, 2025
About the author
Berthold-Georg Englert
24 books1 followerBerthold-Georg Englert is Provost's Chair Professor at the National University of Singapore, and Principal Investigator at the Centre for Quantum Technologies. In 2006, he was recognized for outstanding contributions to theoretical research on quantum coherence. B.-G. Englert's principal research interests concern applications in quantum information science, but he is also known for his early work on quantum optics together with Marlan Scully at Texas A&M University.
Berthold-Georg Englert was American Physical Society Outstanding Referee in 2008, and is presently the Scientific Secretary of the Julian Schwinger Foundation.
Berthold-Georg Englert obtained his Ph.D. in Physics from the University of Tubingen in 1981. He did post-doctoral research at the Technical University Munich and obtained his Dr. rer. nat. habil. in 1990.
He is the author of more than 160 publications in the fields of atomic, molecular and optical physics. His book Symbolism of Atomic Measurements is authoritative in the field of quantum mechanics.
Berthold-Georg Englert was American Physical Society Outstanding Referee in 2008, and is presently the Scientific Secretary of the Julian Schwinger Foundation.
Berthold-Georg Englert obtained his Ph.D. in Physics from the University of Tubingen in 1981. He did post-doctoral research at the Technical University Munich and obtained his Dr. rer. nat. habil. in 1990.
He is the author of more than 160 publications in the fields of atomic, molecular and optical physics. His book Symbolism of Atomic Measurements is authoritative in the field of quantum mechanics.
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