One from many: Estimating a function of many parameters

• URL: http://arxiv.org/abs/2002.02898v2
• Date: Wed, 16 Sep 2020 20:18:13 GMT
• Title: One from many: Estimating a function of many parameters
• Authors: Jonathan A. Gross, Carlton M. Caves
• Abstract summary: Many parameters of a process are unknown; estimate a specific linear combination of these parameters without having the ability to control any of the parameters. Geometric reasoning demonstrates the conditions, necessary and sufficient, for saturating the fundamental and attainable quantum-process bound.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Difficult it is to formulate achievable sensitivity bounds for quantum multiparameter estimation. Consider a special case, one parameter from many: many parameters of a process are unknown; estimate a specific linear combination of these parameters without having the ability to control any of the parameters. Superficially similar to single-parameter estimation, the problem retains genuinely multiparameter aspects. Geometric reasoning demonstrates the conditions, necessary and sufficient, for saturating the fundamental and attainable quantum-process bound in this context.

Related papers

• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry [18.64293022108985]
  We propose a novel and comprehensive approach to optimize the parameters encoding strategies with the aid of antiunitary symmetry. The results showcase the simultaneous achievement of ultimate precision for multiple parameters without any trade-off.
  arXiv  Detail & Related papers  (2024-11-22T13:37:43Z)
• Uncertain Quantum Critical Metrology: From Single to Multi Parameter Sensing [0.0]
  We show how uncertainty in control parameters impacts the sensitivity of critical sensors. For finite-size systems, we establish a trade-off between the amount of uncertainty a many-body probe can withstand while still maintaining a quantum advantage in parameter estimation.
  arXiv  Detail & Related papers  (2024-07-29T11:50:21Z)
• Scaling Exponents Across Parameterizations and Optimizers [94.54718325264218]
  We propose a new perspective on parameterization by investigating a key assumption in prior work. Our empirical investigation includes tens of thousands of models trained with all combinations of threes. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work.
  arXiv  Detail & Related papers  (2024-07-08T12:32:51Z)
• Finding the optimal probe state for multiparameter quantum metrology using conic programming [61.98670278625053]
  We present a conic programming framework that allows us to determine the optimal probe state for the corresponding precision bounds. We also apply our theory to analyze the canonical field sensing problem using entangled quantum probe states.
  arXiv  Detail & Related papers  (2024-01-11T12:47:29Z)
• Fisher information susceptibility for multiparameter quantum estimation [0.23436632098950458]
  Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit. In quantum metrology, the introduction of the Fisher information measurement noise susceptibility now allows to quantify the robustness of measurement. We provide its mathematical definition in the form of a semidefinite program.
  arXiv  Detail & Related papers  (2023-12-04T16:54:01Z)
• PreQuant: A Task-agnostic Quantization Approach for Pre-trained Language Models [52.09865918265002]
  We propose a novel quantize before fine-tuning'' framework, PreQuant. PreQuant is compatible with various quantization strategies, with outlier-aware fine-tuning incorporated to correct the induced quantization error. We demonstrate the effectiveness of PreQuant on the GLUE benchmark using BERT, RoBERTa, and T5.
  arXiv  Detail & Related papers  (2023-05-30T08:41:33Z)
• Tight Cram\'{e}r-Rao type bounds for multiparameter quantum metrology through conic programming [61.98670278625053]
  It is paramount to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.
  arXiv  Detail & Related papers  (2022-09-12T13:06:48Z)
• Multiparameter quantum critical metrology [0.0]
  We argue that quantum criticality may also play a positive role in reducing the incompatibility in the simultaneous estimation of multiple parameters. The antiferromagnetic and ferromagnetic 1-D Ising chain with both transverse and longitudinal fields are analysed.
  arXiv  Detail & Related papers  (2022-03-23T19:00:01Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits [105.54048699217668]
  We propose a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2021-03-15T17:38:33Z)
• On the quantumness of multiparameter estimation problems for qubit systems [0.0]
  We consider several estimation problems for qubit systems and evaluate the corresponding quantumness R. R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cram'er-Rao bound.
  arXiv  Detail & Related papers  (2020-10-23T19:21:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.