Quantum stochastic differential equations and continuous measurements: unbounded coefficients

TL;DR

This paper extends the theory of quantum continuous measurements modeled by quantum stochastic differential equations to include cases with unbounded coefficients, broadening its applicability to more complex quantum systems.

Contribution

It develops a framework for quantum measurements with unbounded operators, previously limited to bounded cases, and demonstrates its application to a quantum optical system.

Findings

Extended the theory to unbounded coefficients in quantum stochastic differential equations.

Validated the framework with the degenerate parametric oscillator example.

Enhanced the mathematical foundation for quantum measurement models.

Abstract

A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of Hudson-Parthasarathy equations with bounded coefficients. By using some results on Hudson-Parthasarathy equations with unbounded coefficients, we are able to extend the theory of quantum continuous measurements to cases in which unbounded operators on the system space are involved. A significant example of a quantum optical system (the degenerate parametric oscillator) is shown to fulfill the hypotheses introduced in the general theory.