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Teleporting quantum Fisher information under Davies-Markovian dynamics

El Anouz, K., El Allati, A.

Published Jan 1, 2022• 0 citations
OpenAlex

Abstract

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.

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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.
Abstract We have investigated the teleportation of quantum Fisher information (QFI) for a single-qubit system by using two different maximally entangled pure states as resources influenced by a Davies-type Markovian environment. According to the definition of QFI, we first derive the explicit analytical results of QFI with respect to the weight parameter and phase parameter under decoherence. Our analytical results show that the teleportation of QFI is seriously affected by two classes of environment, including dissipative and pure dephasing, depending on the parameter of the teleported state during the teleportation process. In particular, for the optimal precision of estimating the weight parameter is only affected by a dissipative environment with temperature, while the precision of estimating the phase parameter is merely influenced by the dephasing environment.
Abstract In this paper, we have investigated the teleportation of quantum Fisher information (QFI) for a single qubit system using a class of X-states as resources influenced by decoherence channels with memory, including amplitude-damping, phase-damping and depolarizing channels. Using the QFI to quantify the quality of teleportation, we first derive the explicit analytical results of QFIs with respect to the weight parameter ( ) and phase parameter ( ) under these decoherence channels, and find that both and are strongly dependent on the initial state’s parameters c i , noisy channel parameters D and , as well as the teleported state’s parameters and . For comparison with the teleportation of the single qubit case, we have also addressed the teleportation of QFI for a two-qubit entanglement system. The results show that , for a single qubit state, is more robust against noisy channels than that for a two-qubit state. However, for a two-qubit state is more robust than that of a single qubit state against noisy channels.
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.
Abstract We analytically investigate the dynamics of quantum Fisher information of two qubits in independent environments for both uncorrelated and entangled input states. Especially, we observe that, in the non-Markovian regime and resonant case, quantum Fisher information of uncorrelated input state vanishes only at discrete time point whereas that of entangled input state can disappear during finite time interval. It shows that quantum Fisher information, which determines the parameter estimation precision, is strongly affected by the environment memory effects, and the advantage of entanglement-enhance metrology no longer exists even for a very short time. We also note that quantum Fisher information for two kinds of input states can be preserved under appropriate qubit-reservoir detuning.
Abstract Quantum Fisher information is introduced as a measure of estimating the teleported information between two users, one of which is uniformly accelerated. We show that the final teleported state depends on the initial parameters, in addition to the gained parameters during the teleportation process. The estimation degree of these parameters depends on the value of the acceleration, the used single mode approximation (within/beyond), the type of encoded information (classic/quantum) in the teleported state, and the entanglement of the initial communication channel. The estimation degree of the parameters can be maximized if the partners teleport classical information.
We investigate the parameter estimation problem in a two-qubit system, in which each qubit is independently interacting with its Markovian environment. We study in detail the sensitivity of the estimation on the decoherence rate γγγ and the two-qubit interaction strength vvv. In particular, the dynamics of quantum Fisher information are employed as a measure to quantify the precision of the estimations. We find that the quantum Fisher information with respect to the decoherence rate scales like t2/[exp⁡(γt)−1]t^2/[\exp(γt)-1]t2/[exp(γt)−1] and exp⁡(−2γt)\exp(-2γt)exp(−2γt) in the unitary limit and the completely decoherent limit, respectively. When we estimate the interaction strength vvv, the quantum Fisher information shows oscillation behavior in term of time. In addition, our results provide further evidence that the entanglement of the input state may not enhance quantum metrology.