Quantum entanglement is one of the most mysterious phenomena in quantum physics. When two particles become entangled, they form a connected system where measuring one particle instantly affects the other, regardless of the distance between them. Einstein famously described this as spooky action at a distance, because it seemed to violate the principle that nothing can travel faster than light.
Before we can understand quantum entanglement, we must first grasp the concept of quantum superposition. In the quantum world, particles can exist in multiple states simultaneously until they are measured. This is famously illustrated by Schrödinger's cat thought experiment, where a cat in a box is considered both alive and dead until observed. Mathematically, we represent this as a linear combination of quantum states, where the particle exists in all possible states with certain probabilities.
To create entangled photon pairs, scientists commonly use a process called spontaneous parametric down-conversion. In this process, a high-energy photon from a laser enters a special nonlinear crystal, such as beta barium borate. Inside the crystal, the photon spontaneously splits into two lower-energy photons that are quantum entangled. This process must obey conservation laws: the total energy and momentum of the original photon equals the sum of the energies and momenta of the two daughter photons. The resulting photon pair shares a quantum state that cannot be described independently.
Bell's theorem is one of the most important results in quantum physics. It shows that no physical theory based on local hidden variables can reproduce all the predictions of quantum mechanics. The theorem establishes mathematical inequalities that must be satisfied by any local realistic theory. However, quantum mechanics predicts correlations that violate these inequalities. Experimental tests using entangled photons and polarization measurements have consistently confirmed these quantum violations, proving that nature is fundamentally non-local.
The most remarkable aspect of quantum entanglement is the instantaneous correlation between measurements on separated particles. When we measure the spin of one entangled particle and find it pointing up, we immediately know that its partner will be found pointing down, no matter how far apart they are. This correlation happens faster than light could travel between the particles, which Einstein found deeply troubling. The measurement statistics show perfect anticorrelation, with the particles always found in opposite states when measured along the same axis.