Classicality without local discriminability: decoupling entanglement and complementarity

Abstract

An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory -- some of them contradicting both Classical and Quantum Theories -- including: cloning, entanglement swapping, dense coding, additivity of classical capacities, non-monogamous entanglement, hypersignaling. We also prove the existence, in the theory, of a universal processor. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by Quantum Theory, most notably: local discriminability, purity of parallel composition of states, and purification. Moreover, we introduce an exhaustive procedure to construct generic operational probabilistic theories, and a sufficient set of conditions to verify their consistency. In addition, we prove a characterisation theorem for the parallel composition rules of arbitrary theories, and specialise it to the case of bilocal-tomographic theories. We conclude pointing out some open problems. In particular, on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, we formulate a no-go conjecture for the existence of a local-realistic ontological model.

arXiv comment24+7 pages, 2 figures, 1 table, plenty of diagrams; section "Conceptual Preview" added in v2; differently from the published version, a table of contents is herein present

References in corpus (36)

• In defense of the epistemic view of quantum states: a toy theory
• Probabilistic theories with purification
• Programmable quantum gate arrays
• A generalized no-broadcasting theorem
• All Teleportation and Dense Coding Schemes
• Almost quantum correlations
• Quasi-quantization: classical statistical theories with an epistemic restriction
• The completeness of quantum theory for predicting measurement outcomes
• Quantum from principles
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Generalized Probability Theories: What determines the structure of quantum theory?
• Limited Holism and Real-Vector-Space Quantum Theory
• Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• The structure of reversible computation determines the self-duality of quantum theory
• No-hypersignaling principle
• The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
• Entanglement and thermodynamics in general probabilistic theories
• Entanglement is an inevitable feature of any non-classical theory
• Entanglement is necessary for emergent classicality in all physical theories
• Efficient universal programmable quantum measurements
• Fermionic computation is non-local tomographic and violates monogamy of entanglement
• If no information gain implies no disturbance, then any discrete physical theory is classical
• Disentangling Nonlocality and Teleportation
• Thermodynamical cost of some interpretations of quantum theory
• Categorical Probabilistic Theories
• Operational axioms for diagonalizing states
• Discord and non-classicality in probabilistic theories
• Classical theories with entanglement
• Leaks: quantum, classical, intermediate, and more
• Fermionic state discrimination by local operations and classical communication
• Hyperdense coding and superadditivity of classical capacities in hypersphere theories
• Cellular automata in operational probabilistic theories
• Categorical Operational Physics
• How dynamics constrains probabilities in general probabilistic theories
• Exploring the limits of no backward in time signalling

Cited by in corpus (16)

• Quantum theory based on real numbers can be experimentally falsified
• General probabilistic theories: An introduction
• A no-go theorem on the nature of the gravitational field beyond quantum theory
• Classical theories with entanglement
• Information and disturbance in operational probabilistic theories
• Measurement incompatibility is strictly stronger than disturbance
• Shannon theory beyond quantum: information content of a source
• Causal influence in operational probabilistic theories
• The signaling dimension of physical systems
• Symmetry-induced failures of tomographic locality: Constructing foil theories by twirling
• Optimal CHSH values for regular polygon theories in generalized probabilistic theories
• Minimal operational theories: classical theories with quantum features
• Which entropy for general physical theories?
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• Information-theoretic derivation of energy, speed bounds, and quantum theory
• Violation of Bell Inequalities: Mapping the Conceptual Implications