Fisher information under decoherence in Bloch representation

Abstract

The dynamics of two variants of quantum Fisher information under decoherence are investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit, by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra $\mathfrak{su}(d)$. By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of phase parameter with the Ramsey interferometry.

16 pages, 4 figures

References in corpus (41)

• Advances in Quantum Metrology
• Quantum metrology
• On the Improvement of Frequency Stardards with Quantum Entanglement
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Quantum spin squeezing
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum entanglement in photosynthetic light harvesting complexes
• Fisher information and multiparticle entanglement
• Multipartite entanglement and high precision metrology
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• The Quantum Chernoff Bound
• Quantum metrology with entangled coherent states
• Exact quantum master equation via the calculus on path integrals
• Quantum Metrology: Dynamics vs. Entanglement
• Spin squeezing and pairwise entanglement for symmetric multiqubit states
• Scaling laws for the decay of multiqubit entanglement
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Exponentially Enhanced Quantum Metrology
• Entanglement Dynamics of Two Qubits in a Common Bath
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Spin squeezing: transforming one-axis-twisting into two-axis-twisting
• Ziv-Zakai Error Bounds for Quantum Parameter Estimation
• Qubit metrology and decoherence
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Sudden vanishing of spin squeezing under decoherence
• Wigner-Yanase information on quantum state space:the geometric approach
• Note on Explicit Formulae for the Bures Metric
• Quantum frequency estimation with trapped ions and atoms
• Optimal Measurement on Noisy Quantum Systems
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Quantum-limited metrology and Bose-Einstein condensates
• Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses
• Quantum states for Heisenberg-limited interferometry
• Spin Squeezing under Non-Markovian Channels by Hierarchy Equation Method
• Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates
• Quantum-limited metrology in the presence of collisional dephasing
• Decoherence and entanglement in a bosonic Josephson junction: Bose-enhanced quantum-Zeno control of phase-diffusion
• Robust multipartite quantum correlations without complex encodings
• Exact quantum dissipative dynamics under external time-dependent fields driving
• Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator

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