The Diminished Quantum Uncertainty in Multipartite Entanglement

Abstract

The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a particle simultaneously, while on the other side, the quantum entanglement renders the entangled quanta lose their independence, including measurements imposed on them. By virtue of the majorization, here we establish a general correlation relation for quantum uncertainty and multipartite entanglement. Within this scheme, the optimization problems for entropy and majorization uncertainty relation are solved. We obtain a diminished uncertainty relation in the presence of multipartite entanglement, where the lower bound is connected with the entanglement class. This result is inspiring, reveals the intrinsic quantitative connection between uncertainty relation and entanglement, and may have a deep impact on quantum measurement in application.