  The quantification of the "measurement uncertainty" aspect of Heisenberg's
Uncertainty Principle---that is, the study of trade-offs between accuracy and
disturbance, or between accuracies in an approximate joint measurement on two
incompatible observables---has regained a lot of interest recently. Several
approaches have been proposed and debated. In this paper we consider Ozawa's
definitions for inaccuracies (as root-mean-square errors) in approximate joint
measurements, and study how these are constrained in different cases, whether
one specifies certain properties of the approximations---namely their standard
deviations and/or their bias---or not. Extending our previous work [C.
Branciard, Proc. Natl. Acad. Sci. U.S.A. 110, 6742 (2013)], we derive new
error-trade-off relations, which we prove to be tight for pure states. We show
explicitly how all previously known relations for Ozawa's inaccuracies follow
from ours. While our relations are in general not tight for mixed states, we
show how these can be strengthened and how tight relations can still be
obtained in that case.
