  In this paper, we prove the equivalence of inserting separable quantum states
and deletions. Hence any quantum code that corrects deletions automatically
corrects separable insertions. First, we describe the quantum
insertion/deletion error using the Kraus operators. Next, we develop an algebra
for commuting Kraus operators corresponding to insertions and deletions. Using
this algebra, we prove the equivalence between quantum insertion codes and
quantum deletion codes using the Knill-Laflamme conditions.
