General quantum-classical dynamics as measurement based feedback

• DOI: 10.21468/scipostphys.17.3.083
• Publication Date: 2024-09-18T13:36:43Z
• Authors: Antoine Tilloy
• Keywords: Quantum Physics; [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]; Physics; QC1-999; FOS: Physical sciences; Quantum Physics (quant-ph); 530; [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]; 510

This note derives the stochastic differential equations and partial differential equation of general hybrid quantum–classical dynamics from the theory of continuous measurement and general (non-Markovian) feedback. The advantage of this approach is an explicit parameterization, without additional positivity constraints. The construction also neatly separates the different effects: how the quantum influences the classical and how the classical influences the quantum. This modular presentation gives a better intuition of what to expect from hybrid dynamics, especially when used to construct possibly fundamental theories.