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.

PROBABILITY REPRESENTATION OF OPTICAL SIGNALS AND NEW ENTROPY OF QUANTUM STATES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1399-1407 ◽  
Author(s):  
MARGARITA A. MAN'KO ◽  
OLGA V. MAN'KO ◽  
VLADIMIR I. MAN'KO
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Probability Distributions ◽  
Quantum States ◽  
Nonlinear Evolution Equations ◽  
Spin States ◽  
Probability Representation ◽  
Optical Signals ◽  
Quantum Optical ◽  
Spin Tomograms

Probability distributions (tomograms) associated to classical and quantum optical signals are introduced. Nonlinear evolution equations are discussed in the probability representation. For spin states, entropy and information corresponding to spin tomograms are studied.

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.

scholarly journals Quantum Generative Adversarial Networks for learning and loading random distributions

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Christa Zoufal ◽  
Aurélien Lucchi ◽  
Stefan Woerner
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Quantum Algorithms ◽  
Probability Distributions ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Simulation ◽  
Quantum States ◽  
Generative Adversarial Networks ◽  
Adversarial Networks

AbstractQuantum algorithms have the potential to outperform their classical counterparts in a variety of tasks. The realization of the advantage often requires the ability to load classical data efficiently into quantum states. However, the best known methods require $${\mathcal{O}}\left({2}^{n}\right)$$O2n gates to load an exact representation of a generic data structure into an $$n$$n-qubit state. This scaling can easily predominate the complexity of a quantum algorithm and, thereby, impair potential quantum advantage. Our work presents a hybrid quantum-classical algorithm for efficient, approximate quantum state loading. More precisely, we use quantum Generative Adversarial Networks (qGANs) to facilitate efficient learning and loading of generic probability distributions - implicitly given by data samples - into quantum states. Through the interplay of a quantum channel, such as a variational quantum circuit, and a classical neural network, the qGAN can learn a representation of the probability distribution underlying the data samples and load it into a quantum state. The loading requires $${\mathcal{O}}\left(poly\left(n\right)\right)$$Opolyn gates and can thus enable the use of potentially advantageous quantum algorithms, such as Quantum Amplitude Estimation. We implement the qGAN distribution learning and loading method with Qiskit and test it using a quantum simulation as well as actual quantum processors provided by the IBM Q Experience. Furthermore, we employ quantum simulation to demonstrate the use of the trained quantum channel in a quantum finance application.

scholarly journals Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

2018 ◽  
Vol 25 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Cosmo ◽  
Domenico Felice ◽  
Stefano Mancini ◽  
Giuseppe Marmo ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Geometric Structure ◽  
Initial Conditions ◽  
Probability Distributions ◽  
End Points ◽  
Quantum Properties ◽  
Statistical Manifolds ◽  
Classical Setting ◽  
Qualitative Effect

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

scholarly journals A new nonclassicality measure for the quantum states of a bosonic field

2019 ◽  
Vol 198 ◽  
pp. 00013
Author(s):  
Stephan De Bièvre ◽  
Dmitri Horoshko ◽  
Giuseppe Patera ◽  
Mikhail Kolobov
Keyword(s):  
Wigner Function ◽  
Probability Distributions ◽  
Quantum States ◽  
Bosonic Field ◽  
Creation And Annihilation Operators ◽  
The Creation

We review a recently proposed measure of the nonclassicality of a bosonic field, based on the sensitivity of its quasi-probability distributions to ordering of the creation and annihilation operators. We illustrate the new measure by several concrete examples and show its advantages compared to other measures of nonclassicality such as the Wigner function negativity and the entanglement potential.

Interference of Quantum States and Superposition Principle in Probability Representation of Quantum Mechanics

2019 ◽  
Vol 26 (03) ◽  
pp. 1950016 ◽  
Author(s):  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distributions ◽  
Superposition Principle ◽  
State Density ◽  
Quantum States ◽  
Density Matrices ◽  
Probability Representation ◽  
Density Operators ◽  
Pure States

The superposition of pure quantum states explicitly expressed in terms of a nonlinear addition rule of state density operators is reviewed. The probability representation of density matrices of qudit states is used to formulate the interference of the states as a combination of the probability distributions describing pure states. The formalism of quantizer–dequantizer operators is developed. Examples of spin-1/2 states and f-oscillator systems are considered.

Neutrosophic Perspective of Neutrosophic Probability Distributions and its Application

2021 ◽  
pp. 96-109
Author(s):  
M. Lathamaheswari ◽  
◽  
◽  
◽  
◽  
...  
Keyword(s):  
Stochastic Process ◽  
Uniform Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Statistical Distributions ◽  
Classical Probability ◽  
Numerical Examples ◽  
Limiting Case ◽  
First Time

Neutrosophical probability is concerned with inequitable and defective topics and processes. This is a subset of Neutrosophic measures that includes a prediction of an event (as opposed to indeterminacy) as well as a prediction of some unpredictability. When there is no such thing as a non-stochastic occurrence, the Neutrosophic probability is the probability of determining a stochastic process. It is a generalisation of classical probability, which states that the probability of correctly predicting an occurrence is zero. Until now, neutrosophic probability distributions have been derived directly from conventional statistical distributions, with fewer contributions to the determination of the for statistical distribution. We introduced the Poission distribution as a limiting case of the Binomial distribution for the first time in this study, and we also proposed Neutrosophic Exponential Distribution and Uniform Distribution for the first time. With numerical examples, the validity and soundness of the proposed notions were also tested.

Sign in / Sign up

Export Citation Format

Share Document