The Essence of Entanglement

Entanglement, according to Erwin Schrödinger the essence of quantum mechanics, is at the heart of the Einstein-Podolsky-Rosen paradox and of the so-called “quantum nonlocality"—the fact that a local realistic explanation of quantum mechanics is not possible as quantitatively expressed by violation of Bell’s inequalities. Even as entanglement gains increasing importance in most quantum information processing protocols, its conceptual foundation is still widely debated. Among the open questions are: What is the conceptual meaning of quantum entanglement? What are the most general constraints imposed by local realism? Which general quantum states violate these constraints? Developing Schrödinger’s ideas in an information-theoretic context, we suggest that a natural understanding of quantum entanglement results when one accepts (1) that the amount of information per elementary system is finite and (2) that the information in a composite system resides more in the correlations than in properties of individuals. The quantitative formulation of these ideas leads to a rather natural criterion of quantum entanglement for pure states, which starts from the amount of information in correlations, rather than the non-factorizability of Hilbert space vectors representing the states. Independently, extending Bell’s original ideas, one can obtain a single general Bell inequality that summarizes all possible constraints imposed by local realism on the correlations for a multi-qubit system, and for situations in which the observers can choose between two (complementary) measurements. Violation of the general Bell inequality results in an independent general criterion for quantum entanglement for multi-qubit states. Most importantly, the two criteria agree in essence, though the two approaches are conceptually very different. This concurrence supports our information-theoretic interpretation of quantum entanglement| and of quantum physics in general.