Picture-Invariance in Quantum Optics

We clarify the controversy over coherent-state (CS) versus number-state (NS) pictures in quantum optics. The NS picture is equivalent to the CS picture, as long as phase φ in laser fields are randomly distributed, as Mølmer argues. However, claim by Rudolph and Sanders [Phys. Rev. Lett. 87, 077903 (2001)] has a few gaps. First they make an assumption that is not necessarily true in calculation of a density operator involved with two-mode squeezed state. We show that there exists entanglement in the density operator without defying the assumption that phases are randomly distributed. Moreover, using a concept of picture-invariance, we argue that it is not that criteria for quantum teleportation are not satisfied. We discuss an analogy between the controversy on the CS versus NS pictures to that on the heliocentric versus geocentric pictures. PACS: 03.65.Ud, 03.67. -a, 03.67.Dd, 42.50. -p, 42.50.Ar