Multiparameter estimation, lower bound on quantum Fisher information and non-Markovianity witnesses of noisy two-qubit systems
arXiv:1812.06172 · doi:10.1007/s11128-019-2446-8
Abstract
By using the quantum Fisher information (QFI), we address the process of \textit{single}-parameter estimation in the presence of bosonic as well as fermionic environments and protection of information against the noise. In particular, the quantum interferometric power (IP) of the evolved state of the system is uncovered as an important lower bound for the QFIs of initially encoded parameters. Moreover, we unveil new witnesses of non-Markovianity, that can be used to detect efficiently the memory effects and backflow of information from the environment to the system. On the other hand, we also investigate the \textit{multiparameter} estimation of initial parameters encoded into the quantum state of a two qubit system and obtain analytical formula of the corresponding QFI matrix. In particular, the corresponding quantum Cramer-Rao bounds in both single and multiparameter estimations are analysed. In addition, we illustrate that the quantum \textit{coherence} and \textit{purity} of the evolved state of the probes are two key elements in realizing optimum multiparameter estimation.
References in corpus (51)
- Advances in Quantum Metrology
- Quantifying Coherence
- Quantum metrology
- Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
- Non-Markovian dynamics in open quantum systems
- Entanglement and non-Markovianity of quantum evolutions
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- On the Improvement of Frequency Stardards with Quantum Entanglement
- Operational Resource Theory of Coherence
- Assessing non-Markovian dynamics
- Robustness of coherence: An operational and observable measure of quantum coherence
- Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
- Characterizing Nonclassical Correlations via Local Quantum Uncertainty
- Intrinsic randomness as a measure of quantum coherence
- Quantum Enhanced Multiple Phase Estimation
- Using entanglement against noise in quantum metrology
- How to quantify coherence: Distinguishing speakable and unspeakable notions
- Fisher information under decoherence in Bloch representation
- Compatibility in Multiparameter Quantum Metrology
- Trace-distance measure of coherence
- Relating the Resource Theories of Entanglement and Quantum Coherence
- The Fidelity and Trace Norm Distances for Quantifying Coherence
- Quantum discord determines the interferometric power of quantum states
- Geometrical characterization of non-Markovianity
- Experimental quantum-enhanced estimation of a lossy phase shift
- Quantum enhanced estimation of a multi-dimensional field
- Foundations and Measures of Quantum Non-Markovianity
- Noisy metrology beyond the standard quantum limit
- Quantum Fisher information for states in exponential form
- Extremal properties of the variance and the quantum Fisher information
- Optimal estimation of joint parameters in phase space
- Introduction to quantum Fisher information
- A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
- Monogamy of quantum correlations - a review
- Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian avataras
- Quantum fisher information in noninertial frames
- Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
- Characterizing non-Markovianity via quantum interferometric power
- Local versus Global Strategies in Multi-parameter Estimation
- Delineating incoherent non-Markovian dynamics using quantum coherence
- Detecting metrologically useful asymmetry and entanglement by a few local measurements
- Multiple phase estimation for arbitrary pure states under white noise
- Environmentally-induced effects on a bipartite two-level system: geometric phase and entanglement properties
- Optimal estimation of entanglement in optical qubit systems
- Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment
- Quantum discord of X-states as optimization of one variable function
- Loss-resistant unambiguous phase measurement
- Quantum sensing of the phase space displacement parameters using a single trapped ion
- Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology
- Werner states and the two-spinors Heisenberg anti-ferromagnet
- Joint estimation of phase and phase diffusion for quantum metrology
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- Quantum thermometry in a squeezed thermal bath
- Ohmic Reservoir-based non-Markovianity and Quantum Speed Limit Time
- Estimating energy levels of a three-level atom in single and multi-parameter metrological schemes
- Coherent control of dissipative dynamics in a periodically driven lattice array
- Memory effects in high-dimensional systems faithfully identified by Hilbert-Schmidt speed-based witness
- Adiabatic Quantum Estimation: A Numerical Study of the Heisenberg XX Model with Antisymmetric Exchange