Estimation of pulsed driven qubit parameters via quantum Fisher information
N Metwally, S S Hassan · Laser Physics Letters · 2017
Abstract We estimate the initial weight and phase parameters ( θ , ϕ ) of a single qubit system initially prepared in the coherent state | θ , ϕ 〉 and in interaction with three different shapes of pulses; rectangular, exponential, and sin 2 -pulses. In general, we show that the estimation degree of the weight parameter depends on the pulse shape and the initial phase angle, ( ϕ ) . For the rectangular pulse case, increasing the estimating rate of the weight parameter via the Fisher information function ( F θ ) is possible with small values of the atomic detuning parameter and larger values of pulse strength. Fisher information ( F ϕ ) increases suddenly at the resonant case to reach its maximum value if the initial phase ϕ = π / 2 and consequently one may estimate the phase parameter with a high degree of precision. If the initial system is coded with classical information, the upper bounds of Fisher information for resonant and non-resonant cases are much larger and consequently, one may estimate the phase parameter with a high degree of accuracy. Similarly, as the detuning increases the Fisher information decreases and therefore the possibility of estimating the phase parameter decreases. For exponential and sin 2 -pulses the Fisher information is maximum ( F θ , ϕ = 1 ) and consequently, one can always estimate the weight and the phase parameters ( θ , ϕ ) with a high degree of precision.