quantumentanglement

Quantumentanglement is a fundamental phenomenon in quantum physics in which the quantum state of two or more systems is inseparable. If the joint state cannot be written as a product of the subsystem states, the systems are entangled. These states exhibit correlations between measurement outcomes that cannot be explained by classical local properties, and the correlations persist across large distances without enabling faster-than-light signaling.

Historically, entanglement arose from discussions of the Einstein-Podolsky-Rosen paradox in 1935, which questioned quantum mechanics’ completeness. Schrödinger highlighted the concept, calling it a defining feature. In 1964, Bell derived inequalities that exclude local realism; quantum mechanics predicts violations for entangled states, a prediction borne out by many experiments.

A canonical example is a pair of spin-1/2 particles in a singlet state or photons produced in polarization-entangled pairs. Measuring one particle yields results that are perfectly anti-correlated with the other along the same basis, while single results are random. Entanglement also extends to more than two parties.

Mathematically, a pure entangled state cannot be factored into a product of subsystem states. The Schmidt decomposition provides a canonical form, and entanglement entropy quantifies the degree of entanglement for bipartite states. Mixed states can be entangled as well, requiring separability criteria to distinguish them from separable states.

As a resource, entanglement enables quantum teleportation, superdense coding, and various quantum cryptographic protocols. It supports quantum networks and computing, though real-world use is limited by decoherence and loss. Ongoing research aims to generate, distribute, and preserve entanglement in scalable systems.