  We show how to optimally discriminate between K distinct quantum states, of
which N copies are available, using one-at-a-time interactions with each of the
N copies. While this task (famously) requires joint measurements on all N
copies, we show that it can be solved with one-at-a-time "coherent
measurements" performed by an apparatus with log(K) qubits of quantum memory.
We apply the same technique to optimal discrimination between K distinct
N-particle matrix product states of bond dimension D, using a coherent
measurement apparatus with log(K) + log(D) qubits of memory.
