Lower bound on the number of Toffoli gates in a classical reversible   circuit through quantum information concepts
  The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information - there is no need for an actual physical quantum computer. The method is illustrated on the example of classical Shannon data compression. 
Sandu Popescu, Berry Groisman and Serge Massar