A Silk Road from Leibniz to Quantum Information

At the roots of quantum physics we find two “specular” principles: a principle of distinguishability, which arranges the “uncertainty” of quantum measurement, and a principle of continuity, which drives the evolution of quantum systems. The vital link between the two principles was sharply captured by Leibniz. In his Theodicy, the issue of continuity (and indivisibles) is presented as one of “the two famous labyrinths” in which our reason can lose its way; the other concerns “the great question of freedom and necessity.” According to Leibniz, only geometry can provide a thread for the labyrinth of continuity. However, escaping from the labyrinth of Fate, Fortune, and Freedom requires a different perspective on nature. Leibniz’s perspective on the mechanism of nature is significantly different from Descartes’ or Newton’s. It reveals notable affinities with the Chinese correlative thinking. Surprisingly, the rationale behind these affinities may find a coherent setting in quantum information.