aqora

Review of Probability and Statistics

Piero Olla

UNITEXT for physicsAug 13, 20142 citations

Quantum Cognition, Neural Oscillators, and Negative Probabilities

J. Acácio de Barros, Gary Oas

This review paper has three main goals. First, to discuss a contextual neurophysiologically plausible model of neural oscillators that reproduces some of the features of quantum cognition. Second, to show that such a model predicts contextual situations where quantum cognition is inadequate. Third, to present an extended probability theory that not only can describe situations that are beyond quantum probability, but also provides an advantage in terms of contextual decision-making. 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.This review paper has three main goals. First, to discuss a contextual neurophysiologically plausible model of neural oscillators that reproduces some of the features of quantum cognition. Second, to show that such a model predicts contextual situations where quantum cognition is inadequate. Third, to present an extended probability theory that not only can describe situations that are beyond quantum probability, but also provides an advantage in terms of contextual decision-making. 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.

Palgrave Macmillan UK eBooksJan 1, 201713 citations

Probability models

Stanley Gudder, Nino Zanghı̀

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BFeb 1, 198413 citations

On complex probabilities

Giorgio Parisi A

Physics Letters BNov 1, 1983416 citations

Quantum Mechanical Probabilities Not Restricted to a Moment of Time

Norifumi L. Yamada

A theoretical aspect of quantum mechanical probabilities is studied. In particular, it is investigated whether quantum mechanical probabilities can be defined for alternatives which are not restricted to a moment of time. Firstly the meaning and the status of this investigation in quantum mechanics are explained. Secondly a general framework is constructed within which we make the investigation. Thirdly a necessary mathematical tool is reviewed and extended. Lastly the general framework is applied to concrete examples with the help of the mathematical tool. Examples of alternatives are found which are not restricted to a moment of time and for which quantum mechanical probabilities can be defined with clear measurement theoretical meanings if an initial condition of the particle belongs to a specific class. (This is the doctoral thesis of the author.)A theoretical aspect of quantum mechanical probabilities is studied. In particular, it is investigated whether quantum mechanical probabilities can be defined for alternatives which are not restricted to a moment of time. Firstly the meaning and the status of this investigation in quantum mechanics are explained. Secondly a general framework is constructed within which we make the investigation. Thirdly a necessary mathematical tool is reviewed and extended. Lastly the general framework is applied to concrete examples with the help of the mathematical tool. Examples of alternatives are found which are not restricted to a moment of time and for which quantum mechanical probabilities can be defined with clear measurement theoretical meanings if an initial condition of the particle belongs to a specific class. (This is the doctoral thesis of the author.)

The science reports of the Tohoku UniversityJan 31, 19920 citations

Quantum probability law from ‘environment-assisted invariance’ in terms of pure-state twin unitaries

Fedor Herbut

Zurek's derivation of the Born rule from envariance (environment-assisted invariance) is retraced in an attempt to present a more detailed derivation, which is extended to encompass the trace-rule form of the quantum probability law in its full generality. The investigation begins by a review presentation of Schmidt decomposition, and a detailed and complete theory of twin unitaries, which are the other face of envariance, and which stand in close connection with twin observables. The trace rule tr( E ρ), with E being an event (projector) and ρ a quantum state (density operator), is derived in five stages. The first three achieve the same as Zurek's derivation of Born's rule, but in a different way, using the full power of twin unitaries. Stage 4 extends the Zurek-like derivation to states (ray projectors) that are not eigenstates of the density operator. Finally, stage 5 utilizes the assumption of continuity of the probability law in the density operators to extend the trace rule to isolated (not correlated) systems.Zurek's derivation of the Born rule from envariance (environment-assisted invariance) is retraced in an attempt to present a more detailed derivation, which is extended to encompass the trace-rule form of the quantum probability law in its full generality. The investigation begins by a review presentation of Schmidt decomposition, and a detailed and complete theory of twin unitaries, which are the other face of envariance, and which stand in close connection with twin observables. The trace rule tr( E ρ), with E being an event (projector) and ρ a quantum state (density operator), is derived in five stages. The first three achieve the same as Zurek's derivation of Born's rule, but in a different way, using the full power of twin unitaries. Stage 4 extends the Zurek-like derivation to states (ray projectors) that are not eigenstates of the density operator. Finally, stage 5 utilizes the assumption of continuity of the probability law in the density operators to extend the trace rule to isolated (not correlated) systems.

arXiv:quant-ph/0611220Journal of Physics A Mathematical and TheoreticalMay 14, 200714 citations

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