entanglements

Entanglements refer to quantum mechanical phenomena in which the quantum states of two or more objects are inseparably linked, such that the state of each object cannot be described independently of the others, regardless of distance. The joint state, called an entangled state, contains correlations that do not factorize into the states of the individual parts. Measurements reveal correlations that cannot be explained by classical local properties. Bell's theorem shows that no local hidden-variable theory can reproduce all quantum predictions; experiments testing Bell inequalities with entangled particles have violated them, with recent loophole-free tests reinforcing the reality of entanglement.

In quantum information, entanglements are a resource enabling tasks such as quantum teleportation, superdense coding, and entanglement-assisted computation and cryptography. They are quantified by measures such as entanglement entropy for pure states, and concurrence or negativity for mixed states.

Common physical realizations include photon pairs produced by spontaneous parametric down-conversion, entangled ions or electrons, and superconducting qubits. Environmental interactions cause decoherence and entanglement decay, posing a major challenge for practical applications.

Beyond physics, entanglements is also used metaphorically to describe complex interdependencies in social, legal, or professional contexts, where the actions or interests of one actor are tied to others.