Local Uncertainty Relations And Entanglement Detection

How to detect the entanglement efficiently in a given state by both theory and experiment is a basic and longstanding problem in entanglement theory. Further more, it is also a precondition when we take quantum entanglement as a physical resource for quantum information engineering. Thus, the study of entanglement detection has great much of academic and practical value.In this thesis, we focus on the bipartite systems and have lucubrated on PPT entanglement detection, which is the most difficulty part of entanglement detection. We have put forward a nonlinear entanglement witness based on Local Uncertainty Relations (LURs) and unnormalized Local Orthogonal Observables (LOOs) and only local measurement (LM) and classical communication (CC) are needed in experiment. Further more, we present an operational PPT entanglement criterion via optimizing this nonlinear entanglement witness. With the help of LURs, this criterion has clear physical meaning: separable states inherit the sum uncertainty from local states (the states of subsystems), implying the composite system is more disordered than local system, while entangled states may violate it. If preprocess the quantum state with the optimal local filtering operation first, then we will get a better entanglement detection with LURs.We also have reformed the structure of LURs and proposed the product-operator LURs, which is similar to entropy inequality with properly observables. We have studied the influence of collective measurement on LURs and find, for some states, one copy is always better than two copies for entanglement detection, while the case of two copies in parallel structure is better than symmetrical structure. Through we may modify this conclusion when consider other states and more than two copies, it is no doubt that different structure of copies will induce different results on entanglement detection. Besides, we conjecture that the violation of LURs also reveal the nonlocality of entangled states like the violation of Bell inequality as it involves only local measurement and classical communication. It is known that LURs can recognize PPT entanglement, thus we may make use of LURs to display the nonlocality of PPT entanglement experimentally.