Quantum entanglement and classical correlation have the same form

Abstract

In agreement with the data, the quantum correlation between spins violates Bell’s inequality by following a cosine curve when one analyzer is rotated relative to the other. In contrast, the linear correlation attributed to hidden variables has never been observed. Besides these well-established facts, we show here that classical covariance, Pearson correlation, between spins projected as up or down on the analyzer axes also follows the cosine form hitherto uniquely ascribed to the quantum mechanical expectation value. The common cause for the classical correlation is the conservation of intrinsic angular momentum that aligns the two spins antiparallel at the breakup. Thus, as long as the spins retain their orientations relative to each other, the measurement of one spin in a chosen frame of reference also discloses the opposite orientation of the other in that frame. Realizing that classical correlation has the same functional form as quantum entanglement sheds light on the foundations of modern physics and quantum computing.