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Acta Physica Polonica A

Quantum Fisher Information of Bipartitions of W States

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

Published Apr 1, 2015• 27 citations
Publisher

Abstract

We study the quantum Fisher information (QFI) of W states and W -like states under decoherence.In particular, we nd that on the contrary to amplitude damping and depolarizing decoherence, a W -like state of 3 qubits obtained by discarding 1 qubit of a genuine W state of 4 qubits is more robust than a genuine W state of 3 qubits under amplitude amplifying and phase damping decoherence.

DOI
10.12693/aphyspola.127.1233

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We study the quantum Fisher information (QFI) of W states and W -like states under decoherence.In particular, we nd that on the contrary to amplitude damping and depolarizing decoherence, a W -like state of 3 qubits obtained by discarding 1 qubit of a genuine W state of 4 qubits is more robust than a genuine W state of 3 qubits under amplitude amplifying and phase damping decoherence.
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.
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.
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.
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
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.
We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for many-body wave functions known analytically in the occupation-number basis, systematic lower bounds to the QFI can be mapped onto expectation values over a classical probability distribution defined by the wave function amplitudes. This mapping enables efficient estimation via Markov-chain Monte Carlo sampling, with a computational cost that scales as a `slow' exponential (ebLe^{b L}ebL with b≲0.6b \lesssim 0.6b≲0.6) and remains manageable for system sizes well beyond exact diagonalization. We specify this framework to Jastrow-Gutzwiller wave functions. We characterize their metrological content by identifying the observables that maximize the QFI and the corresponding scaling with LLL. Then, we analyze the QFI under three physically motivated noise channels: local dephasing, local amplitude damping, and global depolarizing. We compare polynomial and Krylov-based lower bounds across these channels, relating their behavior to the effective rank of the noisy density matrix and to the structure of the operator generating the parameter encoding. The framework extends naturally to other analytically known wave functions and to a broader class of information-theoretic quantities beyond the QFI.