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

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 J{sub z} 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 D{sup 2}/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.

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