Undoing a quantum measurement by erasing information

In their paper “Undoing a weak quantum measurement of a solid state qubit”, Korotkov and Jordan propose experiments to physically undo a measurement of an unknown quantum state. According to textbook quantum measurements, wavefunction collapse is essentially an irreversible process; the measurement record is indelible. Contrary to this conventional wisdom, the authors show that continuous quantum measurements are written in pencil, not in pen. Considering state-of-the-art quantum dot and superconducting structures used in the lab as quantum bits, the authors give explicit experimental procedures to undo quantum measurement. This is done by making a second continuous measurement and waiting until the combined detector output gives no information about the initial quantum state. The information obtained from the first measurement is erased by the second, fully restoring the initial quantum state. The catch is that the undoing procedure is not always successful, so that as the strength of the first measurement grows (giving a particular answer with increasing certainty), the probability of undoing it decreases, finally reaching zero for a textbook quantum measurement. Continuous wavefunction collapse has recently been experimentally observed [Katz, et al., Science 312, 1498 (2006)], providing a promising candidate for verification of this prediction in the near future.