The Universe as a Detector: A Quantum Filtering Formulation of the Di\'osi-Penrose Model

TL;DR

This paper introduces a quantum filtering approach to the Diosi-Penrose model, using space-time homodyning and quantum stochastic calculus to describe gravitationally induced wave-function collapse.

Contribution

It formulates the Diosi-Penrose model within a quantum filtering framework, connecting gravitational collapse to continuous quantum measurement theory.

Findings

Derives a quantum Kushner-Stratonovich equation for the model

Links gravitational collapse to quantum filtering and decoherence

Provides a new perspective on wave-function collapse mechanisms

Abstract

We consider the Di\'osi-Penrose problem but rather than postulating background gravitational fluctuations, we instead consider the quantum filter that arises from space-time homodyning the continuum of output quadrature described in the open quantum stochastic model presented here. This is described by a quantum Kushner-Stratonovich equation, typical of the form appearing in continuous-time collapse of the wave-function models in Quantum Decoherence Theory