Pure-state quantum trajectories for general non-Markovian systems do not exist

TL;DR

This paper critically examines the interpretation of non-Markovian stochastic Schrödinger equations, demonstrating that pure-state quantum trajectories for such systems do not exist as continuous, physically meaningful paths.

Contribution

The authors identify flaws in previous claims that non-Markovian stochastic Schrödinger equations produce true single-system trajectories, clarifying the limitations of their interpretability.

Findings

Diási's proof claiming true trajectories is flawed

Non-Markovian stochastic Schrödinger solutions cannot be joined into consistent trajectories

Pure-state quantum trajectories for non-Markovian systems do not exist

Abstract

Since the first derivation of non-Markovian stochastic Schr\"odinger equations, their interpretation has been contentious. In a recent Letter [Phys. Rev. Lett. 100, 080401 (2008)], Di\'osi claimed to prove that they generate "true single system trajectories [conditioned on] continuous measurement". In this Letter we show that his proof is fundamentally flawed: the solution to his non-Markovian stochastic Schr\"odinger equation at any particular time can be interpreted as a conditioned state, but joining up these solutions as a trajectory creates a fiction.