Entropic uncertainties for joint quantum measurements

We investigate the uncertainty associated with a joint quantum measurement of two spin components of a spin- 1 2 particle and quantify this in terms of entropy. We consider two entropic quantities, the joint entropy and the sum of the marginal entropies, and obtain lower bounds for each of these quantities. For the case of joint measurements where we measure each spin observable equally well, these lower bounds are tight. © 2009 The American Physical Society.