Quantum entanglement

Quantum entanglement is a property of a joint quantum state that cannot be expressed as separate states of its parts. Measurements on entangled parts produce correlations that cannot be explained by independent local states.

Quantum state: A mathematical description that encodes the probabilities of possible outcomes for a quantum system. Entanglement is a property of a joint quantum state, rather than a force between separated objects.
Superposition principle: The quantum rule that permits a system to occupy a linear combination of possible states. Entangled states often combine alternatives that cannot be assigned independently to each subsystem.
Quantum teleportation: A protocol that transfers an unknown quantum state using shared entanglement and classical communication. Shared entanglement enables state transfer without sending the original quantum system.
EPR paradox: A 1935 argument by Einstein, Podolsky, and Rosen that quantum mechanics might be incomplete because of distant correlations. The argument framed entangled correlations as a challenge to the completeness of quantum mechanics.
Classical correlation: A statistical relationship between outcomes that can arise from shared causes or ordinary probability distributions. Classical correlations can be strong, but they obey Bell inequalities under local hidden-variable assumptions.
Tensor product: An operation that combines vector spaces into a space describing composite systems. Composite quantum systems use tensor products, and some resulting states cannot be factored into parts.
Hilbert space: A complete inner-product vector space used to represent quantum states and observables. Entanglement is defined through whether a state vector in a composite Hilbert space factors.
Superdense coding: A protocol that uses shared entanglement to transmit two classical bits by sending one qubit. Entanglement increases the classical information conveyed by a transmitted qubit.
Einstein–Podolsky–Rosen paper: A 1935 paper arguing that quantum mechanics does not provide a complete account of physical reality. Its analysis of correlated particles helped establish the conceptual problem that entanglement addresses.
Quantum entanglement versus separability: The distinction between quantum states that cannot be decomposed into subsystem states and those that can. Separability is the formal alternative to entanglement for composite quantum states.

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