  We consider quantum state tomography with measurement procedures of the
following type: First, we subject the quantum state we aim to identify to a
know time evolution for a desired period of time. Afterwards we perform a
measurement with a fixed measurement set-up. This procedure can then be
repeated for other periods of time, the measurement set-up however remains
unaltered. Given an $n$-dimensional system with suitable unitary dynamics, we
show that any two states can be discriminated by performing a measurement with
a set-up that has $n$ outcomes at $n+1$ points in time. Furthermore, we
consider scenarios where prior information restricts the set of states to a
subset of lower dimensionality. Given an $n$-dimensional system with suitable
unitary dynamics and a semi-algebraic subset $\mathcal{R}$ of its state space,
we show that any two states of the subset can be discriminated by performing a
measurement with a set-up that has $n$ outcomes at $l$ steps of the time
evolution if $(n-1)l\ge 2\dim\mathcal{R}$. In addition, by going beyond unitary
dynamics, we show that one can in fact reduce to a set-up with the minimal
number of two outcomes.
