Collective vs local measurements in qubit mixed state estimation

Details Collective vs local measurements in qubit mixed state estimation Collective vs local measurements in qubit mixed state estimation

2003-07-28

arxiv.org/abs/quant-ph/0307199v3

Phys. Rev. A 69, 010304 (2004)

Physics

Quantum Physics

4 pages, 1 figure, minor style changes, refs. added

Scientific paper

10.1103/PhysRevA.69.010304

We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error in the estimation goes as 1/N. For local measurements we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that standard tomographic techniques lead to an error proportional to $1/N^{1/4}$, while with our optimal data processing it is proportional to $1/N^{3/4}$.

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