Kothari: Jordan's Lemma and quantum computing

Robin Kothari

I will talk about a classic lemma due to Jordan (1875) that is
frequently used in quantum computing.  Jordan's lemma says that given
any two orthogonal projectors, there is a way to partition the
underlying vector space into 1- and 2-dimensional subspaces that are
invariant under the action of both projectors.  This simple lemma has
applications in several areas of quantum computing.  In this talk will
discuss the lemma, its proof, and explain some selected applications in
quantum algorithms and quantum complexity theory.  (Note: This should
not be confused with a different "Jordan's Lemma" in complex analysis.)