scholarly journals Quantum states satisfying classical probability constraints

2006 ◽  
Author(s):  
Elena R. Loubenets
Keyword(s):  
Quantum States ◽  
Classical Probability ◽  
Probability Constraints

scholarly journals Malevich’s Suprematist Composition Picture for Spin States

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 870
Author(s):  
Vladimir I. Man’ko ◽  
Liubov A. Markovich
Keyword(s):  
Probability Distributions ◽  
Classical System ◽  
Quantum States ◽  
Elementary Geometry ◽  
Spin States ◽  
Classical Probability ◽  
Quantum Properties ◽  
Metropolis Monte Carlo ◽  
Single Qudit ◽  
Noncomposite Systems

This paper proposes an alternative geometric representation of single qudit states based on probability simplexes to describe the quantum properties of noncomposite systems. In contrast to the known high dimension pictures, we present the planar picture of quantum states, using the elementary geometry. The approach is based on, so called, Malevich square representation of the single qubit state. It is shown that the quantum statistics of the single qudit with some spin j and observables are formally equivalent to statistics of the classical system with N 2 - 1 random vector variables and N 2 - 1 classical probability distributions, obeying special constrains, found in this study. We present a universal inequality, that describes the single qudits state quantumness. The inequality provides a possibility to experimentally check up entanglement of the system in terms of the classical probabilities. The simulation study for the single qutrit and ququad systems, using the Metropolis Monte-Carlo method, is obtained. The geometrical representation of the single qudit states, presented in the paper, is useful in providing a visualization of quantum states and illustrating their difference from the classical ones.

On a Quantum Model of Brain Activities — Distribution of the Outcomes of EEG-Measurements and Random Point Fields

2012 ◽  
Vol 19 (04) ◽  
pp. 1250025 ◽  
Author(s):  
Karl-Heinz Fichtner ◽  
Kei Inoue ◽  
Masanori Ohya
Keyword(s):  
Stochastic Process ◽  
Probability Theory ◽  
Probability Distributions ◽  
Quantum States ◽  
Random Point ◽  
Quantum Model ◽  
Classical Probability ◽  
Point Configurations ◽  
Point Field ◽  
The Brain

Considering models based on classical probability theory, states of signals in the brain should be identified with probability distributions of certain random point fields representing the configuration of excited neurons. Then the outcomes of EEG-measurements can be considered as random variables being certain functions of that random point field. In practice, specialists use certain statistical methods evaluating the outcomes of the sequence of these measurements. To make these statistical investigations precise, one should know the distribution of the stochastic process on the space of point configurations representing the time evolution of the configuration of excited neurons in the brain. Up to now that distribution is totally unknown. In this paper we consider time evolutions of random point fields as well as the distribution of the outcomes of EEG-measurements related to unitary evolutions of certain quantum states used in [4, 5, 10 – 14] in order to describe activities of the brain.

Geometry of Quantum States

2006 ◽  
Author(s):  
Ingemar Bengtsson ◽  
Karol Zyczkowski
Keyword(s):  
Quantum States

Transport of quantum states of periodically driven systems

1990 ◽  
Vol 51 (8) ◽  
pp. 709-722 ◽  
Author(s):  
H.P. Breuer ◽  
K. Dietz ◽  
M. Holthaus
Keyword(s):  
Quantum States ◽  
Driven Systems ◽  
Periodically Driven

Quantum States & Processes

1994 ◽  
Vol 187 (Part_1) ◽  
pp. 156-156
Author(s):  
H.-J. Unger
Keyword(s):  
Quantum States

“Non-locality”

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum Entanglement ◽  
Quantum States ◽  
Entangled States ◽  
Entangled Quantum States ◽  
Action At A Distance ◽  
Insight Into ◽  
Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

Quantum optics with nitrogen-vacancy centres in diamond

2017 ◽  
Author(s):  
Yiwen Chu ◽  
Mikhail D. Lukin
Keyword(s):  
Optical Properties ◽  
Quantum Information ◽  
Solid State ◽  
Quantum Optics ◽  
Quantum States ◽  
Nitrogen Vacancy ◽  
Common Theme ◽  
External Effects ◽  
Promising Candidate ◽  
Optical Photons

A common theme in the implementation of quantum technologies involves addressing the seemingly contradictory needs for controllability and isolation from external effects. Undesirable effects of the environment must be minimized, while at the same time techniques and tools must be developed that enable interaction with the system in a controllable and well-defined manner. This chapter addresses several aspects of this theme with regard to a particularly promising candidate for developing applications in both metrology and quantum information, namely the nitrogen-vacancy (NV) centre in diamond. The chapter describes how the quantum states of NV centres can be manipulated, probed, and efficiently coupled with optical photons. It also discusses ways of tackling the challenges of controlling the optical properties of these emitters inside a complex solid state environment.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

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