Toward Characterizing Quantum Entanglement via Dichotomy
Abstract
The dichotomy, which divides an object into two, has wide applications in mathematics, computer science, and philosophy. In this paper, inspired by the method of dichotomy, we propose a theoretical framework to characterize quantum entanglement. The basic idea is to start from the most fundamental physical system and perform binary decomposition step by step to establish different types of entangled states. By dividing a parent system into two subsystems, we investigate the relationships between the subsystems under different states of the parent system. We show that entanglement necessarily exists between the two subsystems when the parent system remains unchanged, whereas it may be absent when the parent system changes. Beyond quantum physics, we demonstrate that the dichotomy also has important implications for classical physics.
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