Optimal estimation of a physical observable's expectation value for pure states
arXiv:quant-ph/0512037 · doi:10.1103/PhysRevA.73.062322
Abstract
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged over all pure states distributed in a unitary invariant way. We find that the optimal estimation is "biased", though the optimal measurement is given by successive projective measurements of the observable. The optimal estimate is not the sample average of observed data, but the arithmetic average of observed and "default nonobserved" data, with the latter consisting of all eigenvalues of the observable.
v2: 5pages, typos corrected, journal version
References in corpus (8)
- Quantum Nonlocality without Entanglement
- Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
- Quantum channels showing superadditivity in capacity
- Reexamination of optimal quantum state estimation of pure states
- Aligning Reference Frames Using Quantum States
- Asymptotic estimation theory for a finite dimensional pure state model
- Communication of Spin Directions with Product States and Finite Measurements
- Optimal estimation of quantum observables