  We present a model of discrete quantum evolution based on quantum
correlations between the evolving system and a reference quantum clock system.
A quantum circuit for the model is provided, which in the case of a constant
Hamiltonian is able to represent the evolution over $2^n$ time steps in terms
of just $n$ time qubits and $n$ control gates. We then introduce the concept of
system-time entanglement as a measure of distinguishable quantum evolution,
based on the entanglement between the system and the reference clock. This
quantity vanishes for stationary states and is maximum for systems jumping onto
a new orthogonal state at each time step. In the case of a constant Hamiltonian
leading to a cyclic evolution it is a measure of the spread over distinct
energy eigenstates, and satisfies an entropic energy-time uncertainty relation.
The evolution of mixed states is also examined. Analytical expressions for the
basic case of a qubit clock, as well as for the continuous limit in the
evolution between two states, are provided.
