Even and Odd Schrödinger Cat States in the Probability Representation of Quantum Mechanics

We consider even and odd coherent states (Schrödinger cat states) in the probability representation of quantum mechanics. The probability representation of the cat states is explicitly given using the formalism of quantizer and dequantizer operators, that provides the existence of an invertible map of operators acting in a Hilbert space onto functions called symbols of the operators. We employ a special set of quantizers and dequantizers to construct Wigner functions of the Schrödinger cat states and obtain the relation of the Wigner functions and the probability distributions by means of the Radon integral transform. The notion of entangled classical probability distributions is introduced in probability theory.