Limitations on the Use of the Heisenberg Picture in Quantum Optics

The Heisenberg picture is often used to analyze the performance of optical components, such as a beam splitter or an optical parametric amplifier. We consider a sequence of two or more unitary transformations and show that the Heisenberg operator produced by the first transformation cannot be used as the input to the second transformation [1]. As a result, an inappropriate use of the Heisenberg picture can give misleading or incorrect conclusions. The experimental consequences of this will be illustrated using several examples from quantum optics.

1. J.D. Franson and R.A. Brewster, submitted to Phys. Rev. Lett.