IMPROVED BOUNDS IN THE ENTROPIC UNCERTAINTY AND CERTAINTY RELATIONS FOR COMPLEMENTARY OBSERVABLES

摘要

The entropic uncertainty relation for sets of N+1 complementary observables {A(k)} in N-dimensional Hilbert space, Sigma(k)H(A(k)) greater than or equal to (N + 1) In[1/2(N + 1)], is sharpened to Sigma(k)H(A(k)) greater than or equal to 1/2N In(1/2N) + (1/2N + 1) In(N + 1) for even N. A nontrivial upper bound on the entropy sum (entropic certainty relation) is also obtained for not completely mixed states, while a previously given expression for this bound is proved to hold only when N = 2. [References: 9]