One can read in Wikipedia that quantum correlations are

the expectation value of the product of the outcomes on the two sides

which indicates that $QC(a,b)=\langle( \vec\sigma \cdot \vec a)^{(1)}(\vec\sigma \cdot \vec b)^{(2)} \rangle$ or in classical mechanics represented by hidden variables $\int d\lambda \rho(\lambda)A(a,\lambda)B(b,\lambda)$.

However, in statistics, correlation is strictly defined as $$corr(X,Y)=\frac{cov(X,Y)}{\sigma_X\sigma_Y}= \frac{E(X-\mu_X)E(Y-\mu_Y)}{\sigma_X\sigma_Y} $$

My question:

Is there any relation between the quantum correlation and correlation in statistics? Or are they independent? Sometimes physics definition use the name in math or statistics but refer to different objects which make people confused.


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