RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels

• URL: http://arxiv.org/abs/2008.11178v3
• Date: Wed, 28 Jul 2021 02:15:55 GMT
• Title: RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
• Authors: Vishal Katariya and Mark M. Wilde
• Abstract summary: We study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e., access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels.
• Score: 6.345523830122166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the fundamental tasks in quantum metrology is to estimate multiple parameters embedded in a noisy process, i.e., a quantum channel. In this paper, we study fundamental limits to quantum channel estimation via the concept of amortization and the right logarithmic derivative (RLD) Fisher information value. Our key technical result is the proof of a chain-rule inequality for the RLD Fisher information value, which implies that amortization, i.e., access to a catalyst state family, does not increase the RLD Fisher information value of quantum channels. This technical result leads to a fundamental and efficiently computable limitation for multiparameter channel estimation in the sequential setting, in terms of the RLD Fisher information value. As a consequence, we conclude that if the RLD Fisher information value is finite, then Heisenberg scaling is unattainable in the multiparameter setting.

Related papers

• Robust estimation of the Quantum Fisher Information on a quantum processor [0.0]
  We present the experimental measurement of a series of lower bounds that converge to the quantum Fisher information (QFI) We estimate the QFI for Greenberg-Horne-Zeilinger states, observing genuine multipartite entanglement. We investigate the interplay between state optimization and noise induced by increasing the circuit depth.
  arXiv  Detail & Related papers  (2023-07-31T17:49:04Z)
• Uncertainty Estimation by Fisher Information-based Evidential Deep Learning [61.94125052118442]
  Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. We propose a novel method, Fisher Information-based Evidential Deep Learning ($mathcalI$-EDL) In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focused on the representation learning of uncertain classes.
  arXiv  Detail & Related papers  (2023-03-03T16:12:59Z)
• PD-Quant: Post-Training Quantization based on Prediction Difference Metric [43.81334288840746]
  Post-training quantization (PTQ) is a neural network compression technique that converts a full-precision model into a quantized model using lower-precision data types. How to determine the appropriate quantization parameters is the main problem facing now. PD-Quant is a method that addresses this limitation by considering global information.
  arXiv  Detail & Related papers  (2022-12-14T05:48:58Z)
• Quantum Federated Learning with Entanglement Controlled Circuits and Superposition Coding [44.89303833148191]
  We develop a depth-controllable architecture of entangled slimmable quantum neural networks (eSQNNs) We propose an entangled slimmable QFL (eSQFL) that communicates the superposition-coded parameters of eS-QNNs. In an image classification task, extensive simulations corroborate the effectiveness of eSQFL.
  arXiv  Detail & Related papers  (2022-12-04T03:18:03Z)
• Error Mitigation-Aided Optimization of Parameterized Quantum Circuits: Convergence Analysis [42.275148861039895]
  Variational quantum algorithms (VQAs) offer the most promising path to obtaining quantum advantages via noisy processors. gate noise due to imperfections and decoherence affects the gradient estimates by introducing a bias. Quantum error mitigation (QEM) techniques can reduce the estimation bias without requiring any increase in the number of qubits. QEM can reduce the number of required iterations, but only as long as the quantum noise level is sufficiently small.
  arXiv  Detail & Related papers  (2022-09-23T10:48:04Z)
• Analytical techniques in single and multi-parameter quantum estimation theory: a focused review [0.0]
  This review provides techniques on the analytical calculation of the quantum Fisher information as well as the quantum Fisher information matrix. It provides a mathematical transition from classical to quantum estimation theory applied to many freedom quantum systems.
  arXiv  Detail & Related papers  (2022-04-29T17:29:45Z)
• Limits on Parameter Estimation of Quantum Channels [0.0]
  We study the task of estimating unknown parameters encoded in a quantum channel in the sequential setting. Our goal is to establish lower bounds (called Cramer-Rao bounds) on the estimation error.
  arXiv  Detail & Related papers  (2022-01-05T17:59:04Z)
• Quantum Cram\'er-Rao bound for quantum statistical models with parameter-dependent rank [0.0]
  We argue that the limiting version of quantum Cram'er-Rao bound still holds when the parametric density operator changes its rank. We analyze a typical example of the quantum statistical models with parameter-dependent rank.
  arXiv  Detail & Related papers  (2021-11-01T13:23:04Z)
• 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)
• Quantum Fisher information measurement and verification of the quantum Cram\'er-Rao bound in a solid-state qubit [11.87072483257275]
  We experimentally demonstrate near saturation of the quantum Cram'er-Rao bound in the phase estimation of a solid-state spin system. This is achieved by comparing the experimental uncertainty in phase estimation with an independent measurement of the related quantum Fisher information.
  arXiv  Detail & Related papers  (2020-03-18T17:51:06Z)
• In and out of equilibrium quantum metrology with mean-field quantum criticality [68.8204255655161]
  We study the influence that collective transition phenomena have on quantum metrological protocols. The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
  arXiv  Detail & Related papers  (2020-01-09T19:20:42Z)

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.