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Kluwer Academic Publishers eBooks

Generalised Measurements, Retrodiction and State Manipulation

Stephen Mark Barnett, Anthony Chefles, David Thomas Pegg, Lee S. Phillips

Published Dec 19, 2005• 0 citations
Publisher

Abstract

We develop and discuss noveltypes of generalisedquantum measurement. The associated non-unitary time evolution enables the manipulation of quantum states in ways that are not achievable by unitary operations. Particular emphasis is given to quantum optical realisations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47097-7_17

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We develop and discuss noveltypes of generalisedquantum measurement. The associated non-unitary time evolution enables the manipulation of quantum states in ways that are not achievable by unitary operations. Particular emphasis is given to quantum optical realisations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Different spectral subspaces of a self-adjoint operator T in general entail different behaviors of the unitary evolution group e −itT (particularly as | t |→∞). In this chapter many such dynamical issues are discussed; the main motivation is when T corresponds to the Schrödinger operator of a quantum system. Some related physical concepts, such as quantum return probability and test operators, are used to probe the large-time behaviors. The cornerstones of such results are the concepts of precompactness, almost periodicity and the Wiener and Riemann-Lebesgue lemmas. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Evolution of a Physical State Vector (PSV) is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. Non-local measurements, proposed by Aharanov and Albert, are excluded when the reduction is attributed to measurement devices which are included in the PSV. The existence of a PSV allows to formulate phenomenological laws of reduction. A proposal ismade for which the collapse time is found tobe τ c = bh /Δ E , where Δ E is a difference in energy distribution between alternative world branches. Experiments yield the bounds 1.35·10 11 < b <4.5·10 18 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Prediction, of course, is the making of statements about the likelihood of future events. retrodiction (or postdiction) is the making of statement about past events. In these lectures we shall study the rules governing retrodictive probabilities both in the quantum and classical domains. In doing so we develop a powerful tool with which to interpret physical phenomena and both analyse and interpret experiments. We use retrodictive methods to analyze a number of phenomena in quantum optics including the familiar photon antibunching, entanglement and ghost imaging and the perhaps less familiar ideas of quantum scissors, quantum computation in the past a single-particle analysis of two-particle interference. Quantum retrodiction is a quantitative theory and the familiar techniques for evolving quantum states and modelling open systems are applicable to retrodictive problems, but only with the introduction of some novel features. We conclude with a few remarks on more philosophical issues related to the arrow of time and wavefunction "collapse" in the measurement process. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.