  Landauer's erasure principle states that any irreversible erasure protocol of
a single bit memory needs work of at least $k_B T ln2.$ Recent proof of concept
experiments has demonstrated that the erasure protocols with work close to the
Landauer limit can be devised. Under feedback, where the state of the bit can
be measured, the work needed for bit erasure can be lower than $k_B T ln2.$ In
this article, we analyze the energetics of feedback enabled erasure, while
incorporating the imperfections of experimentally realized memory and bit
erasure protocols that admit failure probabilities. We delineate the role of
uncertainty in measurements and its effects on the work and entropy changes for
a feedback-based erasure. We quantitatively demonstrate that the deficit
between the Landauer limit and the minimum average work needed in a
feedback-based erasure is accounted for by the mutual information between the
measurement and the state of the memory, while incorporating the imperfections
inherent in any realization. We experimentally demonstrate analysis results on
a memory and erasure protocol realized using optical fields.
