Evaluating the quantum Ziv-Zakai bound in noisy environments
arXiv:2203.11436 · doi:10.1364/OE.459659
Abstract
In the highly non-Gaussian regime, the quantum Ziv-Zakai bound (QZZB) provides a lower bound on the available precision, demonstrating the better performance compared with the quantum Cramér-Rao bound. However, evaluating the impact of a noisy environment on the QZZB without applying certain approximations proposed by Tsang [Phys. Rev. Lett. 108, 230401 (2012)] remains a difficult challenge. In this paper, we not only derive the general form of the QZZB with the photon loss and the phase diffusion by invoking the technique of integration within an ordered product of operators, but also show its estimation performance for several different Gaussian resources, such as a coherent state (CS), a single-mode squeezed vacuum state (SMSVS) and a two-mode squeezed vacuum state (TMSVS). Our results indicate that compared with the SMSVS and the TMSVS, the QZZB for the CS always shows the better estimation performance under the photon-loss environment. More interestingly, for the phase-diffusion environment, the estimation performance of the QZZB for the TMSVS can be better than that for the CS throughout a wide range of phase-diffusion strength. Our findings will provide a useful guidance for investigating the noisy quantum parameter estimation.
arXiv comment10 pages, 4 figures
References in corpus (33)
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum Illumination with Gaussian States
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- Quantum limits to dynamical evolution
- Distributed quantum sensing in a continuous variable entangled network
- Multi-parameter estimation in networked quantum sensors
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Optical phase estimation in the presence of phase-diffusion
- Optimal quantum estimation of loss in bosonic channels
- Quantum Metrological Limits via a Variational Approach
- Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
- Ziv-Zakai Error Bounds for Quantum Parameter Estimation
- Quantifying Coherence in Infinite Dimensional Systems
- Interferometric superlocalization of two incoherent optical point sources
- Sub-Heisenberg estimation strategies are ineffective
- Quantum-enhanced metrology for multiple phase estimation with noise
- Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
- Quantum Fisher information from randomized measurements
- Quantum Semiparametric Estimation
- The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
- Ultimate accuracy limit of quantum pulse-compression ranging
- Optimal Distributed quantum sensing using Gaussian states
- Quantum-enhanced data classification with a variational entangled sensor network
- Quantum Metrological Bounds for Vector Parameter
- Quantum limits of superresolution in a noisy environment
- Quantum limit for measurement of a weak classical force coupled to a noisy quantum-mechanical oscillator
- Maximal quantum Fisher information for phase estimation without initial parity
- Quantum Weiss-Weinstein bounds for quantum metrology
- Improving phase estimation using the number-conserving operations
- Precision bounds for noisy nonlinear quantum metrology
- Multiparameter simultaneous optimal estimation with an SU(2) coding unitary evolution
- Generalized Limits for Parameter Sensitivity via Quantum Ziv-Zakai Bound
- Variational Limits for Phase Precision in Linear Quantum Optical Metrology