TITLE:
Classical Correlations vs Quantum Correlations—Similarities, Differences, Opportunities
AUTHORS:
Gunter Meissner, Sidy Danioko, Pedro Villarreal
KEYWORDS:
Classical Correlations, Quantum Correlations, CHSH Framework, Correlation Matrices, Quantum Computing
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.9,
September
30,
2024
ABSTRACT: Classical Correlations were founded in 1900 by Karl Pearson and have since been applied as a statistical tool in virtually all sciences. Quantum correlations go back to Albert Einstein et al. in 1935 and Erwin Schrödinger’s responses shortly after. In this paper, we contrast classical with quantum correlations. We find that classical correlations are weaker than quantum correlations in the CHSH framework. With respect to correlation matrices, the trace of classical correlation matrices is dissimilar to quantum density matrices. However, the off-diagonal terms have equivalent interpretations. We contrast classical dynamic (i.e., time evolving) stochastic correlation with dynamic quantum density matrices and find that the off-diagonal elements, while different in nature, have similar interpretations. So far, due to the laws of quantum physics, no classical correlations are applied to the quantum spectrum. However, conversely, quantum correlations are applied in classical environments such as quantum computing, cryptography, metrology, teleportation, medical imaging, laser technology, the quantum Internet and more.