Reexamination of optimal quantum state estimation of pure states

Abstract

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.

v3(journal version): title changed, presentation improved

References in corpus (11)

• Optimal Quantum Cloning Machines
• Optimal Cloning of Pure States
• Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
• Optimal Cloning of Pure States, Judging Single Clones
• Optimal state estimation for d-dimensional quantum systems
• Quantum copying: Fundamental inequalities
• Minimal optimal generalized quantum measurements
• Aligning Reference Frames Using Quantum States
• Asymptotic estimation theory for a finite dimensional pure state model
• Optimal scheme for estimating a pure qubit state via local measurements
• Communication of Spin Directions with Product States and Finite Measurements

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