It is often said that measuring a systems 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 measurements 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 Heisenbergs 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 measurements outcome.
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