Information-theoretic derivation of energy, speed bounds, and quantum theory

Abstract

We provide a derivation of quantum theory in which the existence of an energy observable that generates the reversible dynamics follows directly from information-theoretic principles. Our first principle is that every reversible dynamics is implementable through a collision model, i.e. a sequence of fast collisions with an array of identically prepared systems. Combined with four additional principles, known as causality, classical decomposability, purity preservation, and strong symmetry, the collision model pins down the quantum framework, sets up a one-to-one correspondence between energy observables and generators of the dynamics, and provides an information-theoretic derivation of the Mandelstam-Tamm bound on the speed of quantum evolutions.

arXiv comment4+36 pages, 1 figure

References in corpus (31)

• Quantum principal component analysis
• Informational derivation of Quantum Theory
• Probabilistic theories with purification
• Unknown Quantum States: The Quantum de Finetti Representation
• Programmable quantum gate arrays
• Thermalizing Quantum Machines: Dissipation and Entanglement
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Quantum collision models: open system dynamics from repeated interactions
• Collision-model-based approach to non-Markovian quantum dynamics
• Quantum Picturalism
• Higher-order interference and single-system postulates characterizing quantum theory
• Collision models can efficiently simulate any multipartite Markovian quantum dynamics
• Simulation of indivisible qubit channels in collision models
• Quantum theory from questions
• Entropy in general physical theories
• Limits on non-local correlations from the structure of the local state space
• The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
• Quantum Theory, namely the pure and reversible theory of information
• Reconstructing quantum theory from diagrammatic postulates
• Dilation of states and processes in operational-probabilistic theories
• Ruling out higher-order interference from purity principles
• Microcanonical thermodynamics in general physical theories
• Operational axioms for diagonalizing states
• Composites and Categories of Euclidean Jordan Algebras
• Classicality without local discriminability: decoupling entanglement and complementarity
• Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
• On defining the Hamiltonian beyond quantum theory
• Unification of energy concepts in generalised phase space theories
• Bell Nonlocality in Classical Systems Coexisting with other System Types