Asymptotic Estimation of a Shift Parameter of a Quantum State

DOI10.1137/S0040585X97981044zbMATH Open1089.81011arXivquant-ph/0307225OpenAlexW2054007546MaRDI QIDQ5700629

Alexander S. Holevo

Publication date: 28 October 2005

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Abstract: We develop an asymptotic theory of estimation of a shift parameter in a pure quantum state to study the relation between entangled and unentangled covariant estimates in the analytically most transparent way. After recollecting basics of estimation of shift parameter in Sec. 2, we study the structure of the optimal covariant estimate in Sec. 3, showing how entanglement comes into play for several independent trials. In Secs. 4,5 we give the asymptotics of the performance of the optimal covariant estimate comparing it with the ``semiclassical unentangled covariant estimation in the regular case of finite variance of the generator of the shift group. Sec. 6 is devoted to covariant estimation in the case where the regularity assumption is violated.

Full work available at URL: https://arxiv.org/abs/quant-ph/0307225

zbMATH Keywords

entanglementquantum estimation theoryshift parametercovariant estimates

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Estimation in multivariate analysis (62H12) Quantum computation (81P68) Estimation and detection in stochastic control theory (93E10) Quantum stochastic calculus (81S25)

Related Items (1)

Estimation of the parameters in a two-state system coupled to a squeezed bath

This page was built for publication: Asymptotic Estimation of a Shift Parameter of a Quantum State

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5700629)