You have a problem, then.
There is an experiment (not an appropriate subject for going into detail on in this thread, there are many references available on the 'Net and a pretty in-depth description on this forum written by yours truly) called the Delayed Choice Quantum Eraser and a related experiment called the Aspect experiment after its creator, and designed quite deliberately as a realization of the Einstein-Podolsky-Rosen experiment by which Einstein sought to show that quantum mechanics could not be a complete description of quantum dynamics, which show quite conclusively according to the overwhelming majority of physicists that Heisenberg Uncertainty is not a matter of us being unable to measure a value, but a matter of the particle in question not actually
having a value of a parameter. If the spin of a particle (for example) on its X axis has been measured, then these experiments show not merely that we
cannot measure the value of the spin on its Y axis, but that it
does not have a value of spin on its Y axis at that time. If we later measure the spin on its Y axis, it will have one, but if many such measurements are made, they will give a quantum distribution, which is a random distribution, not a distribution that agrees with the law of the conservation of angular momentum. It's as if the value of the spin about that second axis was reset somehow by the earlier measurement of the spin about the X axis.
Random IS. The ultimate most basic constituents of reality show random behavior, and in fact if they did not,
we would not see Newton's three Laws of Motion. More to the point, if they did not, we would not see the Second Law of Thermodynamics. This is not a guess, or an assertion; it is a fact. The derivation of the Second Law of Thermodynamics from the random character of quantum interactions is called the Fluctuation Theorem, and you will note that this is a mathematical theorem, not a scientific theory. It is therefore rigorous. The specific requirement for randomness is imposed by two requirements: ergodicity, and time reversal symmetry. These two cannot exist in combination without randomness.
Determinism exists; but it is a matter of the outcome of ensembles of randomly interacting particles. Be certain that you know precisely what you are talking about not believing.
ETA: Forgot to make the main point!
If you know the starting point has to have a truly random distribution, unconstrained by conservation laws, then
by definition the same starting point need not create the same ending, if the outcome is deterministic.