# Continuous quantum measurement and It\^o formalism

## TL;DR

This paper develops a new quantum-stochastic calculus for continuous position measurement, providing a nonlinear differential equation for the quantum state and proposing a physical realization method.

## Contribution

It introduces a novel quantum-stochastic calculus and a nonlinear differential equation for continuous quantum position measurement, along with a physical implementation proposal.

## Key findings

- Derived a new quantum-stochastic differential calculus.
- Formulated a closed nonlinear quantum-stochastic differential equation.
- Proposed a physical realization of continuous position measurement.

## Abstract

A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed particle. Possible physical realization of continuous position measurement is constructed.