# Quantum Entanglement **Entanglement** is a correlation between quantum systems so strong that the whole has a definite state while the parts do not. It is the resource that separates quantum information from classical information. ## First principles Take two [[Qubit|qubits]]. A *separable* (unentangled) state can be written as one qubit's state times the other's. An entangled state cannot. The canonical example is a Bell state: $ |\Phi^+\rangle = \tfrac{1}{\sqrt{2}}\big(|00\rangle + |11\rangle\big) $ Here neither qubit has a state of its own. Yet the moment you measure one and get $0$, the other is instantly guaranteed to be $0$ as well — and the same for $1$. The outcomes are perfectly linked even though each individual outcome is random. > [!intuition] Not faster-than-light signaling > Entanglement does not let you send a message instantly. Each side sees only random results; the correlation is visible only when the two sides later compare notes through an ordinary channel. ## Why it matters for computing - It lets a quantum computer build correlations across many qubits that no classical machine can efficiently track. - It is the glue of [[Quantum Error Correction]]: information is spread across an entangled block of qubits so that no single error can corrupt it. - It is consumed and created by two-qubit operations, whose quality is measured by [[Gate Fidelity]]. ## Related - [[Qubit]] - [[Quantum Error Correction]] - [[Syndrome Extraction]]