On The Study Of Quantum Correlation And Quantum Uncertainty Principle

Measurement-induced nonlocality?MIN?was first introduced by Luo and Fu [1]in 2011.In a broad way,it is always regarded as some kind of quantum correlations.To capture this nonlocal effect induced by local measurements,they defined the MIN in terms of the Hilbert-Schmidt norm,where the maximum is taken over all the von Neumann measurements {K_A^k} which do not disturb ?Alocally,and ???=?_kK_A^k?I?^ABK_A^k?I.In section 3,we introduce a new measure of MIN based on Wigner-Yanase skew information.This definition inherits the nice properties of skew information such as contractivity,which guarantees it to be a good measure.The analytical formulas of MIN based on Wigner-Yanase skew information for any pure states,2 × n-dimensional mixed states,and some higher-dimensional symmetric states are presented.Furthermore,the tight upper bound to MIN based on Wigner-Yanase skew information in the general case is also derived.Weak measurements play a vital role in theoretical and experimental physics[2–7].Weak measurements cause small change to quantum states,and is determined by its strengthen parameter,thereby opening up the possibility of new ways of manipulating and controlling quantum systems.In section 4,we propose a geometric way of quantifyingh quantum discord with weak measurements.It is shown that this geometric measure of quantum discord with weak measurements is linearly dependent on the well known geometric measure of quantum discord [8] and only captures partial quantumness of the states.What is more,we find that the residual quantumness which the weak measurements fail to extract can be extracted by strong measurements on the post-state after weak measurements.It is found that the quantum correlation can be extracted by a sequence of infinitesimal weak measurements.The uncertainty principle is one of the fundamental ideas of quantum mechanics.It sets limits on our ability to predict the outcomes of two incompatible measurements.It was originally formulated by Heisenberg for position and momentum observables [9],and then extended it to two arbitrary observables A and B by Robertson [10].Subsequently,Deutsch [11] advocated for characterizing the ”spread” in the outcomes of two incompatible measurements via Shannon entropies.In section5,we investigate Quantum-memory-assisted entropic uncertainty relations?EUR?based on weak measurements.It is shown that the lower bound of EUR revealed by weak measurements is always larger than that revealed by the corresponding projective measurements.A series of lower bounds of EUR under both weak measurements and projective measurements are presented.Interestingly,the quantum memory-assisted entropic uncertainty relation based on weak measurements is a a monotonically decreasing function of the strength parameter.Furthermore,a series of information theoretic inequalities are also presented.