# Notes on oldest jump unravelling of spatial decoherence master equation

## TL;DR

This paper investigates the oldest known jump unraveling of the spatial decoherence quantum master equation, demonstrating its localization properties and comparing it to more recent diffusive approaches.

## Contribution

It provides a rigorous proof that the orthojump unraveling localizes the quantum state, extending understanding of different stochastic unravellings of the master equation.

## Key findings

- Orthojump unraveling localizes the quantum state.
- It is analytically tractable despite requiring numerical methods.
- Comparison with diffusive unravellings highlights similarities in localization.

## Abstract

Solution of free particle quantum master equation with spatial decoherence can be unravelled into stochastic quantum trajectories in many ways. The first example, published in 1985, proposed a piecewise deterministic jump process for the wave function. While alternative unravellings, diffusive ones in particular, proved to be tractable analytically, the jump process 1985, also called orthojump, allows for few analytic results, it needs numeric methods as well. Here we prove that, similarly to diffusive unravellings, it is localizing the quantum state.