Entangled

Entangled refers to a phenomenon in quantum mechanics known as quantum entanglement, in which the quantum states of two or more objects are interdependent such that the state of each cannot be described independently of the others, regardless of distance. In an entangled system, measurement outcomes exhibit correlations that cannot be explained by classical properties assigned to the individual parts.

Mathematically, a pure state of two or more subsystems is entangled if it cannot be written as a product of states of its parts. Entangled states enable nonlocal correlations that Einstein once called "spooky action at a distance," though they do not allow faster-than-light communication because outcomes remain fundamentally random until comparison is made.

Historically, entanglement arose from the 1935 EPR paper, which argued that quantum predictions implied either incompleteness of quantum mechanics or nonlocal effects. Schrödinger popularized the term entanglement. A key development was Bell's theorem (1964), which shows that no local hidden-variable theory can reproduce all quantum predictions. Experiments testing Bell inequalities, starting with early tests and continuing with closing various loopholes, have supported quantum predictions.

Applications of entanglement include quantum computing, where entangled qubits are used for certain computations; quantum teleportation, which transfers a quantum state using entanglement and classical communication; quantum key distribution and dense coding. Entanglement is fragile: interactions with the environment cause decoherence, gradually destroying correlations, thus sustaining it requires isolation, error correction, or entanglement purification.

Beyond science, entangled describes a general condition of interdependence and is used as a title or descriptor in various works of art and media.