Quantum Trajectories and Their Extremal-probability Paths - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Trajectories and Their Extremal-probability Paths write by Philippe Lewalle. This book was released on 2021. Quantum Trajectories and Their Extremal-probability Paths available in PDF, EPUB and Kindle. "Quantum theory posits that measurements are invasive: It describes an interactive process, mediating all knowledge of quantum properties, in which an observer probes a quantum system and draws inferences about its behavior based on the outcomes they receive. This dissertation emphasizes the theory, and several applications, of time-continuous monitoring of quantum systems. The particular results described below follow two threads: One concerns the behavior of extremal-probability trajectories, derived from a path integral description and action-extremization principle applied to diffusive quantum trajectories. The other concerns the use of continuous measurement for generating and preserving entanglement between two remote qubits. Two new phenomena arising in the optimal paths, derived as the first-order variational solutions of a stochastic action, are presented herein. Multiple solutions which extremize the probability of the measurement record may connect the same initial and final quantum state over the same time interval; these groups of multipath solutions arise as dynamical instabilities in the optimal path dynamics, and in close mathematical analogy with the formation of caustics in optics. Furthermore, the proliferation of these quantum caustics is closely connected to chaotic behavior among extremal-probability paths. This optimal path chaos that we characterize fundamentally relies on measurement, and can occur in a system with no immediate classical analog, such as a qubit; this is in contrast with typical explorations of quantum chaos. The other thread developed herein concerns methods to generate and protect entanglement between two remote qubits by joint continuous measurement of their spontaneous emission. We characterize the entanglement dynamics arising in quantum jump trajectories due to continuous photon counting, as well as in diffusive trajectories arising from homodyne monitoring. These processes generate equivalent entanglement yield on average, despite qualitatively different dynamics in their respective individual realizations. Finally, some strategies for feedback control based on these measurements are developed, with the goal of increasing the entanglement yield and lifetime. Specifically, we illustrate how implement a measurement un-doing and control procedure, that traps the two-qubit dynamics in limit cycles around Bell states for each type of measurements mentioned"--Pages xiii-xiv.
Quantum and Semiclassical Trajectories: Development and Applications
Quantum and Semiclassical Trajectories: Development and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum and Semiclassical Trajectories: Development and Applications write by Yujun Zheng. This book was released on 2023-08-02. Quantum and Semiclassical Trajectories: Development and Applications available in PDF, EPUB and Kindle.
Quantum Probability
Quantum Probability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Probability write by Stanley P. Gudder. This book was released on 2014-06-28. Quantum Probability available in PDF, EPUB and Kindle. Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism. Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles. The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.
Quantum Trajectories and Measurements in Continuous Time
Quantum Trajectories and Measurements in Continuous Time - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Trajectories and Measurements in Continuous Time write by Alberto Barchielli. This book was released on 2009-07-21. Quantum Trajectories and Measurements in Continuous Time available in PDF, EPUB and Kindle. This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output.
The Quantum Theory of Motion
The Quantum Theory of Motion - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Quantum Theory of Motion write by Peter R. Holland. This book was released on 1995-01-26. The Quantum Theory of Motion available in PDF, EPUB and Kindle. An explanation of how quantum processes may be visualised without ambiguity, in terms of a simple physical model.
