Assumptions that imply quantum dynamics is linear

Abstract

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.

10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introduction

References in corpus (1)

• Dynamics of initially entangled open quantum systems

Cited by in corpus (23)

• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
• Fast quantum state discrimination with nonlinear PTP channels
• Action principle for cellular automata and the linearity of quantum mechanics
• Eliminating Ensembles from Equilibrium Statistical Physics: Maxwell's Demon, Szilard's Engine, and Thermodynamics via Entanglement
• Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's Rule
• Quantumness of discrete Hamiltonian cellular automata
• Volumes of conditioned bipartite state spaces
• Nonlinear evolution and signaling
• Why quantum dynamics is linear
• Are nonlinear discrete cellular automata compatible with quantum mechanics?
• Stability of the Grabert master equation
• Hot Fluids and Nonlinear Quantum Mechanics
• What is tested when experiments test that quantum dynamics is linear
• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata
• Quantum models as classical cellular automata
• Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory
• Supercomputer simulations of transmon quantum computers
• On Arguments for Linear Quantum Dynamics
• Fuzzy Topology, Quantization and Gauge Invariance
• Are almost-symmetries almost linear?
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• The mean field approximation and disentanglement
• Nuclear decay parameter oscillations as possible signal of quantum-mechanical nonlinearity and emergent gravity