Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis

Abstract

Rapid purification by feedback—specifically, reducing the mean impurity faster than by measurement alone—can be achieved by choosing the eigenbasis of the density matrix to be unbiased relative to the measurement basis. Here we further examine the protocol introduced by Combes and Jacobs [Phys. Rev. Lett. 96, 010504 (2006)] involving continuous measurement of the observable Jz for a D-dimensional system. We rigorously rederive the lower bound (2/3)(D+1) on the achievable speedup factor and also an upper bound, namely D2/2, for all feedback protocols that use measurements in unbiased bases. Finally, we extend our results to n independent measurements on a register of n qubits and derive an upper bound on the achievable speedup factor that scales linearly with n.