Evolution equation for quantum entanglement

Quantum information technology(1) largely relies on a precious and fragile resource, quantum entanglement, a highly nontrivial manifestation of the coherent superposition of states of composite quantum systems. However, our knowledge of the time evolution of this resource under realistic conditions-that is, when corrupted by environment-induced decoherence is so far limited, and general statements on entanglement dynamics in open systems are scarce(2-11). Here we prove a simple and general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement on passage of either component through an arbitrary noisy channel. The robustness of entanglement-based quantum information processing protocols is thus easily and fully characterized by a single quantity.