Quantum dynamical tunneling breaks classical conserved quantities.

We discover that quantum dynamical tunneling, occurring between phase space regions in a classically forbidden way, can break conserved quantities. We rigorously prove that a conserved quantity in a class of typical pseudointegrable systems can be broken quantum mechanically. We then numerically compute the uncertainties of this broken conserved quantity, which remain nonzero for up to 10^{5} eigenstates and exhibit universal distributions similar to energy level statistics.