Book•
Foundations of quantum mechanics
01 Jan 1968-
About: The article was published on 1968-01-01 and is currently open access. It has received 1949 citations till now. The article focuses on the topics: Quantum dynamics & Gleason's theorem.
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TL;DR: In this paper, the authors seek a quantum-theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval.
Abstract: We seek a quantum‐theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seems to pose a paradox which we call Zeno’s paradox in quantum theory. The relation of this result to that of some previous works and its implications and possible resolutions are briefly discussed. The mathematical transcription of the above‐mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the ge...
1,822 citations
Book•
01 Jan 2009TL;DR: In this paper, the authors present a comprehensive treatment of modern quantum measurement and measurement-based quantum control, which are vital elements for realizing quantum technology, including quantum information, quantum metrology, quantum control and related fields.
Abstract: The control of individual quantum systems promises a new technology for the 21st century – quantum technology. This book is the first comprehensive treatment of modern quantum measurement and measurement-based quantum control, which are vital elements for realizing quantum technology. Readers are introduced to key experiments and technologies through dozens of recent experiments in cavity QED, quantum optics, mesoscopic electronics, and trapped particles several of which are analyzed in detail. Nearly 300 exercises help build understanding, and prepare readers for research in these exciting areas. This important book will interest graduate students and researchers in quantum information, quantum metrology, quantum control and related fields. Novel topics covered include adaptive measurement; realistic detector models; mesoscopic current detection; Markovian, state-based and optimal feedback; and applications to quantum information processing.
1,765 citations
01 Jul 1976
TL;DR: In this paper, a quantum-theoretic expression is sought for the probability that an unstable particle prepared initially in a well-defined state will be found to decay sometime during a given interval.
Abstract: A quantum-theoretic expression is sought for the probability that an unstable particle prepared initially in a well-defined state will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the startling conclusion that an unstable particle which is continuously observed whether it decays will never be found to decay. Since recording the track of an unstable particle (which can be distinguished from its decay products) realizes such continuous observations to a close degree of approximation, the above conclusion poses a paradox which we call Zeno's Paradox in Quantum Theory. Its implications and possible resolutions are briefly discussed. The mathematical transcription of the above-mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the general formulation and the proof given here are believed to be new. The known ''no-go'' theorem concerning the semigroup law for the reduced evolution of any physical system (including decaying systems) is subsumed under the theorem as a direct corollary.
1,460 citations
TL;DR: Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics as mentioned in this paper, showing that essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a single experimental arrangement.
Abstract: Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics. The theorem shows that essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a single experimental arrangement. Moreover, the predictions by those theories must significantly differ from those by quantum mechanics. Experimental results evidently refute the theorem's predictions for these theories and favour those of quantum mechanics. The conclusions are philosophically startling: either one must totally abandon the realistic philosophy of most working scientists, or dramatically revise out concept of space-time.
1,285 citations
TL;DR: In this paper, quantum jump, Monte Carlo wave function, and quantum-trajectory methods are discussed and applied to a number of current problems in quantum optics, and relate them to ensemble descriptions.
Abstract: Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schr\"odinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions.
1,232 citations