General quantum-classical dynamics as measurement based feedback

Abstract

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.

arXiv comment14 + 6 pages

References in corpus (36)

• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Dynamical Reduction Models
• A Straightforward Introduction to Continuous Quantum Measurement
• Non-Markovian Quantum State Diffusion
• Measurements continuous in time and a posteriori states in quantum
• The non-Markovian stochastic Schrodinger equation for open systems
• Underground test of gravity-related wave function collapse
• A classical channel model for gravitational decoherence
• Sourcing semiclassical gravity from spontaneously localized quantum matter
• Linear quantum state diffusion for non-Markovian open quantum systems
• Qubit models of weak continuous measurements
• Collapse models with non-white noises
• Pure-state quantum trajectories for general non-Markovian systems do not exist
• Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
• The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory
• Bounds on quantum communication via Newtonian gravity
• Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity
• Principle of least decoherence for Newtonian semi-classical gravity
• Neutron star heating constraints on wave-function collapse models
• Collapse Models: a theoretical, experimental and philosophical review
• Events and Piecewise Deterministic Dynamics in Event-Enhanced Quantum Theory
• The Open Quantum Brownian Motion
• The weak field limit of quantum matter back-reacting on classical spacetime
• Does gravity have to be quantized? Lessons from non-relativistic toy models
• Binding quantum matter and space-time, without romanticism
• Exact signal correlators in continuous quantum measurements
• On GKLS dynamics for local operations and classical communication
• Interacting quantum field theories as relativistic statistical field theories of local beables
• Markovian dynamics for a quantum/classical system and quantum trajectories
• The two classes of hybrid classical-quantum dynamics
• Covariant path integrals for quantum fields back-reacting on classical space-time
• Correlation functions for realistic continuous quantum measurement
• Anomalous contribution to galactic rotation curves due to stochastic spacetime
• Path integrals for classical-quantum dynamics
• Renormalisation of postquantum-classical gravity

Cited by in corpus (11)

• The Diósi-Penrose model of classical gravity predicts gravitationally induced entanglement
• The classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity
• Markovian dynamics for a quantum/classical system and quantum trajectories
• Entanglement in Markovian hybrid classical-quantum theories of gravity
• Exploring the Effects of Mass Dependence in Spontaneous Collapse Models
• Hybrid Classical-Quantum Newtonian Gravity with stable vacuum
• Can gravity mediate the transmission of quantum information?
• Restoring the second law to classical-quantum dynamics
• Probing the nonclassical dynamics of a quantum particle in a gravitational field
• A healthier stochastic semiclassical gravity: world without Schrödinger cats
• Diffusion Minimization via Optimal Smearing in Collapse and Hybrid Classical-Quantum Gravitational Models