Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics

Abstract

We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.

Keywords

• probability distribution
• dequantizer and quantizer operators
• symplectic tomography
• even and odd cat states
• entanglement