Unlearning quantum information

Measurement can drive quantum dynamics, for example in ancilla driven quantum computation where unitary evolution is generated by measurements that extract no information. Where a measurement does reveal some information about the system, it may sometimes be possible to “unlearn” this information and restore unitary evolution through subsequent measurements. Here we analyse two methods of quantum “unlearning” and present a simplified proof of the bound on the probability of successfully applying the required correction operators. The probability of successful recovery is inversely related to the ability of the initial measurement to exclude the possibility of a state. As a consequence there exist unrecoverable measurements that provide little information gain.