Collective versus local measurements in a qubit mixed-state estimation

Abstract

We discuss the problem of estimating a qubit mixed state. We give the optimal estimation 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 varies as [Formula Presented] For local measurements, we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that the error using plain tomography varies as [Formula Presented] while our approach leads to an error proportional to [Formula Presented]. © 2004 The American Physical Society.