Picture Invariance in Quantum Optics

Abstract

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.Dd, 42.50.Ar Besides continuing controversies over its implication on our understanding about physical world [1, 2, 3, 4, 5], quantum mechanics is still revealing its hidden aspects, now in a form of quantum information processing [6].Coherent-state (CS) picture has been successful in describing quantum optical phenomena [7,8,9]. However, the fact that a picture is successful does not exclude possibility of other pictures. Indeed it is not that the CS picture is the only choice [10].Quantum teleportation (QT) [11] is an interesting ingredient of quantum information processing: Utilizing nonlocality of Einstein-Podolsky-Rosen pairs of [1,2,3] quantum bits (qubits), QT enables us to do a task whose result is equivalent to actual transportation of qubits. Recently, a quantum optical experiment was performed by Furusawa et al [12] to demonstrate continuousvariable version [13,14] of QT.