scholarly journals Correlations in a system of classical-like coins simulating spin-1/2 states in the probability representation of quantum mechanics

2019 ◽  
Vol 73 (1) ◽  
Author(s):  
Vladimir N. Chernega ◽  
Olga V. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Representation

scholarly journals Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

2019 ◽  
Vol 1 (2) ◽  
pp. 130-150 ◽  
Author(s):  
Igor Ya. Doskoch ◽  
Margarita A. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Particle System ◽  
Superposition Principle ◽  
Quantum States ◽  
Particle State ◽  
Probability Representation ◽  
Tomographic Probability ◽  
Born’S Rule ◽  
System States

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

scholarly journals Probability representation of quantum mechanics and star product quantization

2019 ◽  
Vol 1348 ◽  
pp. 012101 ◽  
Author(s):  
V N Chernega ◽  
S N Belolipetskiy ◽  
O V Man’ko ◽  
V I Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Star Product ◽  
Probability Representation ◽  
Product Quantization

scholarly journals PT -Symmetric Qubit-System States in the Probability Representation of Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1702 ◽  
Author(s):  
Vladimir N. Chernega ◽  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Explicit Form ◽  
Probability Distributions ◽  
Energy Eigenvalue ◽  
Pt Symmetry ◽  
Eigenvalue Equation ◽  
Probability Representation ◽  
Qubit System ◽  
New Energy ◽  
System States

PT-symmetric qubit-system states are considered in the probability representation of quantum mechanics. The new energy eigenvalue equation for probability distributions identified with qubit and qutrit states is presented in an explicit form. A possibility to test PT-symmetry and its violation by measuring the probabilities of spin projections for qubits in three perpendicular directions is discussed.

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.

scholarly journals Properties of Quantizer and Dequantizer Operators for Qudit States and Parametric Down-Conversion

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 131
Author(s):  
Peter Adam ◽  
Vladimir A. Andreev ◽  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko ◽  
Matyas Mechler
Keyword(s):  
Quantum Mechanics ◽  
Probability Distributions ◽  
Probability Representation ◽  
Density Operators ◽  
Parametric Down Conversion ◽  
Down Conversion

We review the method of quantizers and dequantizers to construct an invertible map of the density operators onto functions including probability distributions and discuss in detail examples of qubit and qutrit states. The biphoton states existing in the process of parametric down-conversion are studied in the probability representation of quantum mechanics.

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