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arXiv · 1005.4230

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

Joshua Combes·Howard M. Wiseman·Kurt Jacobs·Anthony J. O'Connor
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Abstract

Rapid-purification by feedback --- specifically, reducing the mean impurity faster than by measurement alone --- can be achieved by making 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. {\bf 96}, 010504 (2006)] involving continuous measurement of the observable $J_z$ for a $D$-dimensional system. We rigorously re-derive the lower bound $(2/3)(D+1)$ on the achievable speed-up factor, and also an upper bound, namely $D^2/2$, 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 speed-up factor that scales linearly with $n$.

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Joshua Combes, Howard M. Wiseman, Kurt Jacobs, Anthony J. O'Connor. 2010-11-27. Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis. https://doi.org/10.1103/physreva.82.022307

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