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arXiv:1705.04516 · Laser Physics Letters

Estimation of pulsed driven qubit parameters via quantum Fisher information

N Metwally, S S Hassan

Published Oct 30, 2017• 22 citations
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Abstract

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.

DOI
10.1088/1612-202x/aa86e4

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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.
We use a rectangular pulse to freeze the possibility of estimating the coherent parameters (θ, [Formula: see text]) of a single qubit, the local information, and the fidelity of the driven qubit. The possibility of freezing these three quantities depends on the initial state settings and the strength of the pulse. It is shown that the freezing areas increase as the detuning increases, while they decrease at smaller values of the pulse strength. Moreover, as the Fisher information reaches its minimum bounds, the local information and the fidelity are maximized. We show that, when the Fisher information is completely frozen, the pulsed local information and the fidelity are frozen. The freezing degree depends on the initial detuning and the pulse strength. Our results show that, despite the initial and final states of the system being different, the amount of local information is independent of the initial state of the system. These results may be useful in the context of quantum cryptography, teleportation, and secure communication.
We use a rectangular pulse to freeze the possibility of estimating the coherent parameters (θ,ϕθ,ϕθ,ϕ) of a single qubit and the encoded information. It is shown that, as the possibility of estimating the parameters increases, the amount of encoded information decreases. The pulse strength and the detuning between the qubit and the pulse have a different effect on the estimation degree and the encoded information. We show that if the weight parameter, θθθ is estimated, the encoded information depends on the initial state settings. Meanwhile, the encoded information doesn't depend on the estimated phase parameter,ϕϕϕ. These results may be useful in the context of quantum cryptography, teleportation and secure communication.
The dynamics of a charged two-qubit system prepared initially in a maximum entangled state is discussed, where each qubit interacts independently with a dephasing channel. The Fisher information is used to estimate the channel and the energy parameters. Moreover, the contribution from different parts of Fisher information is discussed. We show that, the degree of estimation of any parameter depends on the initial value of this parameter. It turns out that the upper bounds of Fisher information with respect to the dephasing parameter increase and that corresponding to coupling parameter decreases as the initial energy of each qubit increases.
In this paper, Fisher information for an accelerated system initially prepared in the X-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states, is derived for the general state and for Werner state. It is shown that the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the X-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state’s parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.
Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation－quantum Cramer-Rao bound－shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. The initial probing state is the direct product state of qubit and radiation field in which Fock state, thermal state and coherent state are taken into account respectively. We calculate the quantum Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.
The Quantum Fisher information (QFI) of a two charged qubits system that interacts locally with a dephasing channel is quantified with respect to the charged qubits’ and the channel’s parameters. The behavior of Fisher information displays different phenomena as; the sudden changes (increasing/decreasing); the gradual decay and freezing of the QFI. It is shown that the QFI of the dephasing parameter decays gradually and vanishes completely as one increases the initial energies of the qubits and their mutual energy. The possibility of estimating the charged qubits’ energies may be maximized at smaller values of the initial dephasing’s parameter. The estimation degree of the mutual information reaches its upper bounds by increasing the initial energies. It is depicted that, by controlling the qubits’ and the channel’s parameters, the QFI may be frozen. We expect that this result may be interesting in the context of quantum encoding and quantum cryptography.