Taming singularities of the quantum Fisher information
arXiv:2108.05976 · doi:10.1142/S0219749921400049
Abstract
Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.
17 pages
References in corpus (9)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Optimal quantum estimation of loss in bosonic channels
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states
- On quantumness in multi-parameter quantum estimation
- Experimental multiphase estimation on a chip
- General expressions for the quantum Fisher information matrix with applications to discrete quantum imaging
- Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology
- Multiphase estimation without a reference mode
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