  It is often said that measuring a system's position must disturb the
complementary property, momentum, by some minimum amount due to the Heisenberg
uncertainty principle. Using a "weak-measurement", this disturbance can be
reduced. One might expect this comes at the cost of also reducing the
measurement's precision. However, it was recently demonstrated that a sequence
consisting of a weak position measurement followed by a regular momentum
measurement can probe a quantum system at a single point, with zero width, in
position-momentum space. Here, we study this "joint weak-measurement" and
reconcile its compatibility with the uncertainty principle. While a single
trial probes the system with a resolution that can saturate Heisenberg's limit,
we show that averaging over many trials can be used to surpass this limit. The
weak-measurement does not trade-away precision, but rather another type of
uncertainty called "predictability" which quantifies the certainty of
retrodicting the measurement's outcome.
