Entanglement and thermodynamics in general probabilistic theories

Abstract

Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement and exploit it to define entanglement measures in the general probabilistic framework. In addition, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).

24 pages, 4 figures, improved presentation, references added, many new results

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Cited by in corpus (40)

• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Quantum from principles
• General probabilistic theories: An introduction
• A Resource Theory for Work and Heat
• A no-go theorem on the nature of the gravitational field beyond quantum theory
• Generalised phase kick-back: the structure of computational algorithms from physical principles
• Ultimate data hiding in quantum mechanics and beyond
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Thermodynamics and the structure of quantum theory
• Reconstructing quantum theory from diagrammatic postulates
• Ruling out higher-order interference from purity principles
• Categorical Probabilistic Theories
• Operational axioms for diagonalizing states
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Microcanonical thermodynamics in general physical theories
• Entropy, majorization and thermodynamics in general probabilistic theories
• Entanglement in macroscopic systems
• Oracles and query lower bounds in generalised probabilistic theories
• Classicality without local discriminability: decoupling entanglement and complementarity
• Non-classical correlations in quantum mechanics and beyond
• Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator
• Agents, subsystems, and the conservation of information
• On defining the Hamiltonian beyond quantum theory
• Universal structure of objective states in all fundamental causal theories
• Information-theoretic foundations of thermodynamics in general probabilistic theories
• Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure
• Complete Characterization of Entanglement Embezzlement
• How dynamics constrains probabilities in general probabilistic theories
• Compositional resource theories of coherence
• Causal influence in operational probabilistic theories
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• A no-go theorem for theories that decohere to quantum mechanics
• Covariant influences for finite discrete dynamical systems
• The operational reality of quantum nonlocality
• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
• Complete extension: the non-signaling analog of quantum purification
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
• One-shot and asymptotic classical capacity in general physical theories