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量子レトロディクションと履歴

K.-I. Izawa, T. Taniguchi

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

We further see the content and consistency of our claims on retrodictive aspects of quantum theory based on the previous papers, which deal with quantum mechanics of a single particle in one-dimensional space under successive mearsurements of particle position and momentum as a wave packet. The content of retrodiction can be best understood as statements on the past recorded in the present state. Conditional probabilites with the past and future states specified are consistently obtained through the ordinary predictive and/or our retrodictive probability formula in any combined way.

Related papers

量子論におけるレトロディクション I

K.-I. Izawa, T. Taniguchi

We consider retrodictive aspects of quantum theory. As a first step, we adopt quantum mechanics of a single free particle in one-dimensional space. Under successive mearsurements of particle position and momentum as a wave packet, we derive estimation on retrodictive probability, which happens to coincide with the expression for predictive probability into the past.

•Jan 1, 2017•0 citations

量子論におけるレトロディクションII

K.-I. Izawa, T. Taniguchi

We continue to investigate retrodictive aspects of quantum theory based on the previous paper numbered I. We now proceed to consider quantum mechanics of a single interacting particle in one-dimensional space. Under successive mearsurements of particle position and momentum as a wave packet, we argue that a piecewise approximation to the particle motion, when applicable, results in the classical retrodiction just as it results in the classical prediction.

•Jan 1, 2018•0 citations

Retrodiction in quantum theory: I

Izawa Ken'ichi, Taniguchi Tomonori

•Jan 1, 2017•0 citations

Quantum Retrodiction

Stephen Mark Barnett, John Jeffers, David Thomas Pegg +2 more

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.

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Symmetry of Physical Laws. Part III. Prediction and Retrodiction

Satosi Watanabé

An attempt is made within the framework of the accepted quantum physics to achieve the maximum parallelism between prediction (inference of the future observational data from the present ones) and retrodiction (inference of the past observational data from the present ones). To implement this program, it is shown that the "retrodictive state function" (extrapolation of the present data to the past) can be just as useful as the ordinary "predictive state function" (extrapolation of the present data to the future). This leads to a formalism in which time-reversal becomes a linear transformation and double time-reversal becomes a $c$-number. In spite of this formal symmetry, it can be shown that the actual success of a retrodiction depends on the satisfaction of an additional condition which is not required in prediction, and which is not always fulfilled. From the same point of view, a logical loophole is pointed out in the indiscriminate application of the $H$-theorem to the past. The so-called irreversibility of observation is interpreted in terms of the decrease of "information" in the process of inference.

Reviews of Modern Physics•Apr 1, 1955•127 citations
We further see the content and consistency of our claims on retrodictive aspects of quantum theory based on the previous papers, which deal with quantum mechanics of a single particle in one-dimensional space under successive mearsurements of particle position and momentum as a wave packet. The content of retrodiction can be best understood as statements on the past recorded in the present state. Conditional probabilites with the past and future states specified are consistently obtained through the ordinary predictive and/or our retrodictive probability formula in any combined way.
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.
La théorie des probabilités et la théorie quantique, l’une mathématique et l’autre physique, s’apparentent dans la mesure où chacune admet plusieurs interprétations fort différentes. Certains ont proposé que les problèmes conceptuels de la théorie quantique puissent être, sinon résolus, du moins atténués par une interprétation adéquate des probabilités. Nous montrerons plutôt, à travers un survol historique et analytique des probabilités et de la théorie quantique, que si certaines interprétations de l’une et de l’autre s’agencent particulièrement bien, aucune ne s’impose de façon unique. * * * The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum theory could be, if not resolved, at least mitigated by a proper interpretation of probabilities. We rather show, through a historical and analytical overview of probabilities and quantum theory, that if some interpretations of the one and the other go along particularly well, none follows in a unique way.
An attempt is made within the framework of the accepted quantum physics to achieve the maximum parallelism between prediction (inference of the future observational data from the present ones) and retrodiction (inference of the past observational data from the present ones). To implement this program, it is shown that the "retrodictive state function" (extrapolation of the present data to the past) can be just as useful as the ordinary "predictive state function" (extrapolation of the present data to the future). This leads to a formalism in which time-reversal becomes a linear transformation and double time-reversal becomes a ccc-number. In spite of this formal symmetry, it can be shown that the actual success of a retrodiction depends on the satisfaction of an additional condition which is not required in prediction, and which is not always fulfilled. From the same point of view, a logical loophole is pointed out in the indiscriminate application of the HHH-theorem to the past. The so-called irreversibility of observation is interpreted in terms of the decrease of "information" in the process of inference.