Complementary observables and uncertainty relations

Abstract

Two observables A and B of an n-level system (i.e., a quantum system with n-dimensional state space) are called complementary, if knowledge of the measured value of A implies maximal uncertainty of the measured value of B, and vice versa. Such observables exist for all n, but no classification (up to equivalence) of all possible pairs of complementary observables is known except for n\ensuremath{\le}4. Complementary observables are conjectured to satisfy an ``entropic'' uncertainty relation of the strongest possible form. This relation has been verified for n\ensuremath{\le}4 by explicit calculations. A recent attempt of substantiating the widespread interpretation of uncertainty relations in terms of mutual disturbances between measurements is criticized.