entangment

Entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects become linked so that the state of each object cannot be described independently of the others, regardless of the distance between them. In an entangled state, the joint state cannot be factored into a product of individual states. This leads to correlations between measurements on the subsystems that cannot be explained by classical statistics alone.

A common example is a two-qubit Bell state, such as (|00> + |11>)/√2, which is maximally entangled. Measuring one qubit immediately influences the possible outcomes for the other, producing correlations that persist even when the qubits are far apart. The strongest implications were highlighted by the Einstein-Podolsky-Rodol, Rosen, and Schrödinger discussions, and formalized by Bell’s theorem, which shows that no local hidden-variable theory can reproduce all quantum predictions.

Experiments with photons, ions, and superconducting circuits have demonstrated entanglement and violations of Bell inequalities, reinforcing the quantum description. Entanglement is a key resource in quantum information science and underlies several protocols, including quantum teleportation, in which a quantum state is transmitted using entanglement and classical communication; quantum key distribution, notably the Ekert protocol; and dense coding, which can increase classical communication capacity.

Challenges remain, as entanglement is fragile and degrades due to decoherence and loss during transmission. Practical use over long distances motivates research into quantum repeaters and error correction. Entanglement remains central to understanding and exploiting nonclassical correlations in quantum mechanics.