Dynamical Mappings of Density Operators in Quantum Mechanics

1961 ◽  
Vol 2 (6) ◽  
pp. 772-775 ◽  
Author(s):  
Thomas F. Jordan ◽  
E. C. G. Sudarshan
Keyword(s):  
Quantum Mechanics ◽  
Density Operators

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.

Dynamical Mappings of Density Operators in Quantum Mechanics. II. Time Dependent Mappings

1962 ◽  
Vol 3 (5) ◽  
pp. 848-852 ◽  
Author(s):  
Thomas F. Jordan ◽  
Mark A. Pinsky ◽  
E. C. G. Sudarshan
Keyword(s):  
Quantum Mechanics ◽  
Time Dependent ◽  
Density Operators
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