We study the changes in quantum Fisher information (QFI) values for one quantum system consisting of a superposition of W and GHZ states. In a recent work [6], QFI values of this mentioned system studied. In this work, we extend this problem for the changes of QFI values in some noisy channels. We show the change in QFI depending on noise parameters. We report interesting results for different type of decoherence channels.
We study the changes in quantum Fisher information (QFI) values for one quantum system consisting of a superposition of W and GHZ states. In a recent work [6], QFI values of this mentioned system studied. In this work, we extend this problem for the changes of QFI values in some noisy channels. We show the change in QFI depending on noise parameters. We report interesting results for different type of decoherence channels.
Quantum fisher information of a parameter characterizing the sensitivity of a state with respect to parameter changes. In this paper, we study the quantum fisher information of the W state for four, five, six and seven particles in decoherence channels, such as amplitude damping, phase damping and depolarizing channel. Using Krauss operators for decoherence channels components, we investigate the quantum fisher information quite analytically. We observe that for the W state, the amount of the quantum fisher information and consequently, the amount of entanglement are reduced by applying the quantum noises, which affect each particle in the same way. In some cases, a relative increase appears in the quantum fisher information for certain values of the decay strength p. We also show that the phase damping channel vanishes the value of the quantum fisher information for the W state.
Abstract Quantum entanglement lies at the heart of quantum information and quantum metrology. In quantum metrology, with a colossal amount of quantum Fisher information (QFI), entangled systems can be ameliorated to be a better resource scheme. However, noisy channels affect the QFI substantially. This research work seeks to investigate how QFI of N-qubit Greenberger-Horne-Zeilinger (GHZ) state is affected when subjected to decoherence channels: bit-phase flip (BPF) and generalize amplitude damping (GAD) channels, which can be induced experimentally. We determine the evolution under these channels, deduce the eigenvalues, and then derive the QFI. We found that when there is no interaction with the environment, the Heisenberg limit can be achieved via rotations along the z direction. It has been shown that in BPF channel, the maximal mean QFI of the N-qubit GHZ state ( Fˉmax F ¯ m a x ) dwindles as decoherence rate (p B ) increases due to flow of information from the system to the environment, until p B = 0.5, then revives to form a symmetric around p B = 0.5. Thus, p B > 0.5 leads to a situation where more noise yields more efficiency. We found that in GAD channel, at finite temperature, QFIs decay more rapidly than at zero temperature. Our results also reveal that QFI can be enhanced by adjusting the temperature of the environment.
Abstract From the perspective of nonlocal operation, we investigate the Quantum Fisher information of N-qubit W and GHZ superposition state. Taking advantage of the general Ising model and Lipkin-Meshkov-Glick model, we analytically present the QFI of N-qubit superposition state. Evidently the traditional fixed QFI is changed and largely increased. As an paradigm, we numerically study the QFI of 3-qubit superposition state with respect to ratio α and interaction strength ε, and find the trends of QFI in both models are similar. There always exists a turning point for QFI and the α is around 0.7. Interestingly, for the interaction strength ε = 1 in Ising model, the well-known Heisenberg limit is almost achieved for all α. Moreover, under the same interaction strength, we compare the QFI of N-qubit superposition state in both models. With the increasing qubits involved, the α for maximal QFI in Ising model is changed from close to 1 to the middle region, while it is different in Lipkin-Meshkov-Glick model and the α is close to 1.
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.
Abstract Various quantum states have been suggested to realize high-precision measurement and quantum Fisher information (QFI) is one of the most important indicators to evaluate the performance. Here, we systematically investigate the QFI of an N-qubit maximal sliced (MS) state in different environments. In the ideal situation, we present the analytical QFI and it decays from N2 to (N − 1)2 as the parameter α changed from 0 to 1, which denotes the decreased metrological ability. In the amplitude damping channel, the variation trends of QFI with respect to p are similar and it decreases to the number of qubits N at p = 1, meaning the vanished entanglement superiority. However, it is different in the phase damping channel where with the increase of the number of qubits a turning point of QFI equal to N is found at p closing to 0.1. In the Ising-type interacting model, with the increasing interaction strength γ, the QFI with respect to α shows a crossover from decreasing to increasing. Particularly, at the critical point γ = 1, the QFI of an N-qubit MS state is found analytically equal to N2 and regardless of α. This indicates a great potential in achieving the Heisenberg-limited metrology and may shed some new light on quantum information science. PACS: 03.67.-a, 03.65.Ud
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.