Polarization Requirements for Ensemble Implementations of Quantum   Algorithms with a Single Bit Output
  We compare the failure probabilities of ensemble implementations of quantum algorithms which use pseudo-pure initial states, quantified by their polarization, to those of competing classical probabilistic algorithms. Specifically we consider a class algorithms which require only one bit to output the solution to problems. For large ensemble sizes, we present a general scheme to determine a critical polarization beneath which the quantum algorithm fails with greater probability than its classical competitor. We apply this to the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%. 
Brandon M. Anderson (1), David Collins (2) ((1) University of Texas at   Dallas, (2) Bucknell University)