ABSTRACT:
i) The quantum mechanics of higher order parametric amplifiers is studied. It is shown that these devices produce meaningful quantum states; numerical calculations are performed that demonstrate the convergence of matrix elements associated with these states. Further, the correspondence between the classical and quantum evolution for these devices is studied and the differences explained by a kind of "quantum diffusion." Finally, the possibility of producing ordinary squeezed light with these devices is noted.

ii) The generation of squeezed light always involves some scheme that amounts to pumping electromagnetic modes at near twice their natural frequency. When the pump is itself treated quantum mechanically, extra noise is introduced that ultimately limits the amount of squeezing achievable. Detailed calculations are carried out in this regard for the parametric amplifier. It is found that the pump's initial phase noise is responsible for this limit.

iii) Quantum-mechanical measurements are usually described by applying the standard quantum rules to a measurement model. They can also be described by a formalism that uses mathematical objects called Effects and Operations. These two descriptions should be equivalent. D'Espagnat has raised a question about the usage of this formalism of Effects and Operations for repeated measurements. This question is cleared up, and the source of the discrepancy is given a simple interpretation.

iv) Usually, an inequality that is chained becomes a weaker inequality. Chaining the Bell inequality, however, leads to stronger violations by quantum mechanics. Further, a new kind of Bell inequality, based on the information obtained in a measurement, is derived. This information Bell inequality can be used to formulate tests of local realism in very general circumstances, e.g., higher spin versions of the EPR experiment. These new inequalities yield an interpretation for the size of their violation and lead to the formulation of a hierarchy of Bell inequalities for which two-particle Bell inequalities play a special role.