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An Isaac Newton Institute Workshop

Quantum Statistics - quantum measurements, estimation and related topics

Estimation of qubit mixed states with local measurements

Authors: Ramon Munoz-Tapia ( Universitat Autonoma de Barcelona ), Emili Bagan ( Universitat Autonoma de Barcelona )


I discuss the problem of estimating an unknown qubit mixed state from a large sample of N identically prepared states with local measurements. I use as a prior the Bures distribution and focus, for simplicity, on states belonging to the equatorial plane of the Bloch sphere. I will show that the average fidelity for a large sequence of fixed measurements tends to 1-1/N^{3/4}. This is a very suprising result that contrast with both, estimation of pure states and estimation of mixed states with collective measurements, where the fidelity tends to 1 as 1/N.