Improving Polynomial Phase Parameter Estimation by Using Nonuniformly Spaced Signal Sample Methods

2012 ◽  
Vol 60 (7) ◽  
pp. 3405-3414 ◽  
Author(s):  
P. O'Shea
Keyword(s):  
Parameter Estimation ◽  
Phase Parameter ◽  
Polynomial Phase ◽  
Signal Sample

scholarly journals Parameter estimation of qubit states with unknown phase parameter

2015 ◽  
Vol 13 (01) ◽  
pp. 1450044 ◽  
Author(s):  
Jun Suzuki
Keyword(s):  
Parameter Estimation ◽  
Logarithmic Derivative ◽  
Mean Square ◽  
Level System ◽  
Optimal Measurement ◽  
Unknown Phase ◽  
Phase Parameter ◽  
Qubit System ◽  
Mean Square Errors ◽  
Qubit States

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér–Rao (CR) bound and Hayashi–Gill–Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

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