We review and expand on recent advances in theory and experiments concerning
the problem of wavefunction uncollapse: Given an unknown state that has been
disturbed by a generalized measurement, restore the state to its initial
configuration. We describe how this is probabilistically possible with a
subsequent measurement that involves erasing the information extracted about
the state in the first measurement. The general theory of abstract measurements
is discussed, focusing on quantum information aspects of the problem, in
addition to investigating a variety of specific physical situations and
explicit measurement strategies. Several systems are considered in detail: the
quantum double dot charge qubit measured by a quantum point contact (with and
without Hamiltonian dynamics), the superconducting phase qubit monitored by a
SQUID detector, and an arbitrary number of entangled charge qubits.
Furthermore, uncollapse strategies for the quantum dot electron spin qubit, and
the optical polarization qubit are also reviewed. For each of these systems the
physics of the continuous measurement process, the strategy required to ideally
uncollapse the wavefunction, as well as the statistical features associated
with the measurement is discussed. We also summarize the recent experimental
realization of two of these systems, the phase qubit and the polarization
qubit.Comment: 19 pages, 4 figure