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Acta Physica Polonica A

Behavior of Quantum Fisher Information of Bell Pairs under Decoherence Channels

Fatih Özaydin, Azmi Ali Altıntaṣ, Sinan Bugu, Can Yesilyurt

Published Jan 1, 2014• 19 citations
Publisher

Abstract

Quantum Fisher information has recently been an essential tool for analyzing the phase sensitivity of the quantum states in various quantum tasks, requiring high precision, such as quantum clock synchronization, positioning and many applications which include quantum interferometers.Due to the interactions with the environment, all quantum systems are subject to various decoherence eects.Therefore the research on quantum Fisher information under decoherence has been recently attracting more attention.In this work, analyzing the quantum Fisher information, we study the phase sensitivity of bipartite quantum correlations, in particular four Bell pairs amplitude damping channels.For a specic Bell state we arrive at similar results of GreenbergerHorneZeilinger (GHZ) states (as expected).For the other three Bell states, we present our results which point the interesting behavior of quantum Fisher information with respect to the decoherence rate.We also nd the regions where the quantum Fisher information exhibits discontinuities.

DOI
10.12693/aphyspola.125.606

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Quantum Fisher information has recently been an essential tool for analyzing the phase sensitivity of the quantum states in various quantum tasks, requiring high precision, such as quantum clock synchronization, positioning and many applications which include quantum interferometers.Due to the interactions with the environment, all quantum systems are subject to various decoherence eects.Therefore the research on quantum Fisher information under decoherence has been recently attracting more attention.In this work, analyzing the quantum Fisher information, we study the phase sensitivity of bipartite quantum correlations, in particular four Bell pairs amplitude damping channels.For a specic Bell state we arrive at similar results of GreenbergerHorneZeilinger (GHZ) states (as expected).For the other three Bell states, we present our results which point the interesting behavior of quantum Fisher information with respect to the decoherence rate.We also nd the regions where the quantum Fisher information exhibits discontinuities.
We give the explicit expressions of quantum Fisher information and skew information for a two-qubit Bell states. We investigate their dynamics under the decoherence effects: phase-damping channel, depolarizing channel and amplitude-damping channel. We also discuss the thermal entanglement quantified by Wootters concurrence for these three decoherence channels and we compare its dynamical behavior with the quantum Fisher information and skew information. We then use this comparison to investigate the influence of noisy channels on thermal entanglement and its role in boosting the performance of metrology protocols. It is shown that the correlations in two-qubit Bell states are more resistant to phase-damping channel and depolarizing channels.
Quantum Fisher information of a parameter characterizes the sensitivity of the state with respect to changes of the parameter. In this article, we study the quantum Fisher information of a state with respect to SU(2)\mathrm{SU}(2)SU(2) rotations under three decoherence channels: the amplitude-damping, phase-damping, and depolarizing channels. The initial state is chosen to be a Greenberger-Horne-Zeilinger state of which the phase sensitivity can achieve the Heisenberg limit. By using the Kraus operator representation, the quantum Fisher information is obtained analytically. We observe the decay and sudden change of the quantum Fisher information in all three 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{\bar{F}}_{max}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 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