Reexamination of optimal quantum state estimation of pure states

Details Reexamination of optimal quantum state estimation of pure states Reexamination of optimal quantum state estimation of pure states

2004-10-26

arxiv.org/abs/quant-ph/0410207v3

Phys. Rev. A 72, 032325 (2005)

Physics

Quantum Physics

v3(journal version): title changed, presentation improved

Scientific paper

10.1103/PhysRevA.72.032325

A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by M. Hayashi in terms of an infinite set of covariant positive operator valued measures (POVM's) and by Bruss and Macchiavello establishing a connection to optimal quantum cloning. An explicit condition for POVM measurement operators for optimal estimators is obtained, by which we construct optimal estimators with finite POVM using exact quadratures on a hypersphere. These finite optimal estimators are not generally universal, where universality means the fidelity is independent of input states. However, any optimal estimator with finite POVM for M(>N) copies is universal if it is used for N copies as input.

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