Non-Orthogonal Bases for Quantum Metrology
arXiv:1906.00845 · doi:10.1088/1751-8121/ab3fe0
Abstract
Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the analytical evaluation of the quantum Fisher information may be greatly simplified by bypassing both the diagonalization of the density matrix and the orthogonalization of the basis. The key ingredient in our method is the Gramian matrix (i.e. the matrix of scalar products between basis elements), which may be interpreted as a metric tensor for index contraction. As an application, we derive novel analytical results for several estimation problems involving noisy Schroedinger cat states.
arXiv comment9 pages, 2 figures, comments welcome
References in corpus (67)
- Quantum entanglement
- Advances in Quantum Metrology
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- The elusive Heisenberg limit in quantum enhanced metrology
- Quantum computation with optical coherent states
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Confining the state of light to a quantum manifold by engineered two-photon loss
- Quantum metrology with entangled coherent states
- Quantum limits in optical interferometry
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- Quantum enhanced measurements without entanglement
- Quantum Enhanced Multiple Phase Estimation
- Quantum criticality as a resource for quantum estimation
- Individual quantum probes for optimal thermometry
- Compatibility in Multiparameter Quantum Metrology
- Multi-parameter Quantum Metrology
- Quantum fidelity for arbitrary Gaussian states
- Quantum parameter estimation using general single-mode Gaussian states
- Quantum parameter estimation using general single-mode Gaussian states
- Optical phase estimation in the presence of phase-diffusion
- Optimal quantum estimation of loss in bosonic channels
- A new approach to the Cramer-Rao type bound of the pure state model
- Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution
- Noisy metrology beyond the standard quantum limit
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
- Thermometry in the quantum regime: Recent theoretical progress
- Schrodinger cats and their power for quantum information processing
- The ultimate precision limits for noisy frequency estimation
- Weak force detection with superposed coherent states
- Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
- Optimal quantum estimation in spin systems at criticality
- Ultimate precision bound of quantum and sub-wavelength imaging
- Quantum Fisher information for states in exponential form
- Optimal phase measurements with pure Gaussian states
- Optimal estimation of joint parameters in phase space
- Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
- Multiparameter Gaussian Quantum Metrology
- Quantum Limits of Thermometry
- Discontinuities of the quantum Fisher information and the Bures metric
- Using polarons for sub-nK quantum non-demolition thermometry in a Bose-Einstein condensate
- Qubit thermometry for micromechanical resonators
- High photon number path entanglement in the interference of spontaneously downconverted photon pairs with coherent laser light
- Simple expression for the quantum Fisher information matrix
- Ultimate Precision of Adaptive Noise Estimation
- Gaussian systems for quantum enhanced multiple phase estimation
- Precision thermometry and the quantum speed limit
- Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment
- Qubit-assisted thermometry of a quantum harmonic oscillator
- Interferometric superlocalization of two incoherent optical point sources
- Towards superresolution surface metrology: Quantum estimation of angular and axial separations
- Quantum probes for the cutoff frequency of Ohmic environments
- Bounds on Quantum Multiple-Parameter Estimation with Gaussian State
- Quantum limited superresolution of an incoherent source pair in three dimensions
- Ultimate limits for quantum magnetometry via time-continuous measurements
- Continuous-variable quantum probes for structured environments
- Entangling measurements for multiparameter estimation with two qubits
- Entanglement is not very useful for estimating multiple phases
- Quantum estimation of a two-phase spin rotation
- Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder Interferometer
- Efficient representation of Gaussian states for multi-mode non-Gaussian quantum state engineering via subtraction of arbitrary number of photons
- Multi-mode Entanglement is Detrimental to Lossy Optical Quantum Metrology
- Quantum Probes for Ohmic Environments at Thermal Equilibrium
- Enhancement of parameter estimation by Kerr interaction
- Probing the diamagnetic term in light-matter interaction
- Quantum enhanced estimation of diffusion
- Joint estimation of phase and phase diffusion for quantum metrology
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- Fundamental limits of pulsed quantum light spectroscopy: Dipole moment estimation
- Resource theory of superposition: State transformations
- Noiseless Linear Amplification and Loss-Tolerant Quantum Relay using Coherent State Superpositions
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- Generalization of Rayleigh's Criterion on Parameter Estimation with Incoherent Sources
- Enhancing precision thermometry with nonlinear qubits
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