We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$
by a single quantum state $|\Psi \rangle$ of size $O(n)$ qubits,
such that:
for any constant $k$ and any $i_1,...,i_k \in \{1,...,2^n\}$,
the values of the bits $a_{i_1},...,a_{i_k}$ can be retrieved
from $|\Psi \rangle$ by a one-round Arthur-Merlin interactive ... more >>>

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number of measurements that grows only linearly with n. Besides possible ... more >>>