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

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

2010-05-23

arxiv.org/abs/1005.4230v2

Phys. Rev. A 82, 022307 (2010)

Physics

Quantum Physics

v2: published version

Scientific paper

10.1103/PhysRevA.82.022307

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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