Quantum Entanglement and Bell's Theorem: Foundations, Experimental Tests, and Applications in Quantum Information Science

सार

Quantum entanglement, once dismissed by Einstein as "spooky action at a distance," has developed from a philosophical curiosity into a rigorously tested physical phenomenon and a foundational resource for modern quantum technology. This paper reviews the theoretical foundations of entanglement, beginning with the Einstein-Podolsky-Rosen (EPR) argument for the incompleteness of quantum mechanics and Schrödinger's identification of entanglement as its defining feature. It then presents Bell's theorem and the Clauser-Horne-Shimony-Holt (CHSH) inequality, which together transformed the EPR debate from a matter of interpretation into an experimentally decidable question. The paper surveys the experimental tests of Bell's inequality, from the early photon-correlation experiments of Freedman and Clauser and the time-varying-analyzer experiments of Aspect to the loophole-free tests of 2015, which jointly closed the locality and detection loopholes and confirmed the violation of local realism to high statistical significance. Building on this foundation, the paper examines entanglement as a quantifiable physical resource and surveys its central applications in quantum information science: quantum key distribution, quantum teleportation, quantum computing, and quantum-enhanced metrology. The paper concludes by identifying open challenges — decoherence, scalable entanglement distribution, and the residual interpretive questions that Bell tests leave unresolved — that continue to shape current research in the field.