Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
arXiv:1003.4575 · doi:10.1007/s00220-011-1239-4
Abstract
In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the minimum mean square error decreases with the order O(1/n).
In this revision, some unlcear parts are clarified
References in corpus (10)
- Beating the Standard Quantum Limit with Four Entangled Photons
- Entanglement-free Heisenberg-limited phase estimation
- Magnetic field sensing beyond the standard quantum limit using 10-spin NOON states
- Beating the standard quantum limit: Phase super-sensitivity of N-photon interferometers
- Fast rate estimation of an unitary operation in SU(d)
- Fourier Analytic Approach to Phase Estimation
- Phase estimation with photon number constraint
- N-body-extended Channel Estimation for Low-Noise Parameters
- On metric of quantum channel spaces
- On the First Order Asymptotic Theory of Quantum Estimation