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arXiv:1612.03324

Fisher information of two superconducting charge qubits under dephasing noisy

Hamada El-Shiekh Nour Zidan, NASSER METWALLY

Published Dec 10, 2016• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1612.03324

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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.
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.
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.
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.
The estimation degree of a teleported state using two different quantum channels by means of quantum Fisher information is discussed. It consists of using two different noisy channels generated from an interaction between an open quantum system and its surrounding environment under Davies-Markovian dynamics. However, when small interacted system–environment parameters and a small number of detuning parameters are taken into account, a robust estimation degree is obtained. Moreover, it is possible to estimate various system–environment parameters related to the energy relaxation time and dephasing time. By controlling these parameters, we conclude that maximally entangled channels and robust estimation degrees by means of quantum Fisher information are achieved when the energy relaxation and dephasing times vanish.
In this paper, an accelerated two-qubit system initially prepared in maximum or partial entangled state, which interacts locally with white/color or white-color noises, is considered. Due to the acceleration process and the noise effect, the entanglement degraded. Therefore, the effect of noise strength, initial state settings and the acceleration on the survival entanglement are investigated by means of the concurrence. Moreover, the initial parameters that describe this system are estimated by using the quantum Fisher information, where two forms are considered, namely by using a single and two-qubit forms. It is shown that, by using the two-qubit form, the estimation degree of these parameters is larger than that displayed by using a single-qubit form.
The dynamics of entanglement of two superconducting charge qubit system interacting with a squeezed coherent state were examined by means of linear entropy. The influence of the relative phase of the two qubits' levels and squeezing parameter on the time evolution of linear entropy was discussed. The results showed that the linear entropy almost tends to zero at half the revival time when the two qubits were initially in the maximally entangled state. It was also showed that a greater number of oscillations of the linear entropy were observed with the increasing of squeezing parameter and the sustainment time of the maximum entropy was increased. There was no change in the maximum value of the linear entropy. Moreover,the relative phase of the two qubits' levels decreased the degree of entanglement between the two qubits and the field.