Entanglement and superposition are equivalent concepts in any physical theory

Abstract

We prove that any two general probabilistic theories (GPTs) are entangleable, in the sense that their composite exhibits either entangled states or entangled measurements, if and only if they are both non-classical, meaning that neither of the state spaces is a simplex. This establishes the universal equivalence of the (local) superposition principle and the existence of global entanglement, valid in a fully theory-independent way. As an application of our techniques, we show that all non-classical GPTs exhibit a strong form of incompatibility of states and measurements, and use this to construct a version of the BB84 protocol that works in any non-classical GPT.

arXiv comment11 pages, 3 figures

References in corpus (28)

• Quantum entanglement
• Introducing Quantum Discord
• Bell nonlocality
• Informational derivation of Quantum Theory
• Probabilistic theories with purification
• Measures and applications of quantum correlations
• The uncertainty principle determines the non-locality of quantum mechanics
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• An Invitation to Quantum Incompatibility
• Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
• One-to-one mapping between steering and joint measurability problems
• Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
• Generalized Probabilistic Theories Without the No-Restriction Hypothesis
• Comparing the degrees of incompatibility inherent in probabilistic physical theories
• Degree of Complementarity Determines the Nonlocality in Quantum Mechanics
• Ultimate data hiding in quantum mechanics and beyond
• Steering, incompatibility, and Bell inequality violations in a class of probabilistic theories
• Entanglement is necessary for emergent classicality in all physical theories
• Entanglement is an inevitable feature of any non-classical theory
• All measurements in a probabilistic theory are compatible if and only if the state space is a simplex
• Entangleability of cones
• Incompatible measurements in a class of general probabilistic theories
• Conditions on the existence of maximally incompatible two-outcome measurements in General Probabilistic Theory
• Classical theories with entanglement
• Universal gaps for XOR games from estimates on tensor norm ratios
• The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer
• Compatibility of any pair of 2-outcome measurements characterizes the Choquet simplex

Cited by in corpus (18)

• Entanglement entropy, single-particle occupation probabilities, and short-range correlations
• Testing the quantum nature of gravity without entanglement
• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Incompatibility of observables, channels and instruments in information theories
• Unbounded quantum backflow in two dimensions
• Postselected quantum hypothesis testing
• Partial coherence versus entanglement
• Cohering and decohering power of massive scalar fields under instantaneous interactions
• Generalized dynamical theories in phase space and the hydrogen atom
• Characterizing the superposition of arbitrary random quantum states and a known quantum state
• A Post-Quantum Associative Memory
• Spin-Energy Entanglement of a Time-Focused Neutron
• Relating CP divisibility of dynamical maps with compatibility of channels
• Classifying Entanglement by Algebraic Geometry
• The surprising persistence of time-dependent quantum entanglement
• Comparing quantum incompatibility of device sets from an operational perspective
• Decoupling local classicality from classical explainability: A noncontextual model for bilocal classical theory and a locally-classical but contextual theory
• One-shot and asymptotic classical capacity in general physical theories