Related papers: Cram\'er-Rao bound and quantum parameter estimation with non-Hermitian systems

Cram\'er-Rao bound and quantum parameter estimation with non-Hermitian systems

URL: http://arxiv.org/abs/2103.07099v1
Date: Fri, 12 Mar 2021 06:07:40 GMT
Title: Cram\'er-Rao bound and quantum parameter estimation with non-Hermitian systems
Authors: Jianning Li, Haodi Liu, Zhihai Wang, Xuexi Yi
Abstract summary: The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram'er-Rao bound. We derive two previously unknown expressions for quantum Fisher information, and two Cram'er-Rao bounds lower than the well-known one are found for non-Hermitian systems.
Score: 0.37571834897413164
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less attention has been paid to non-Hermitian systems. In this Letter, working with different logarithmic operators, we derive two previously unknown expressions for quantum Fisher information, and two Cram\'er-Rao bounds lower than the well-known one are found for non-Hermitian systems. These lower bounds are due to the merit of non-Hermitian observable and it can be understood as a result of extended regimes of optimization. Two experimentally feasible examples are presented to illustrate the theory, saturation of these bounds and estimation precisions beyond the Heisenberg limit are predicted and discussed. A setup to measure non-Hermitian observable is also proposed.

Related papers

Observing tight triple uncertainty relations in two-qubit systems [21.034105385856765]
We demonstrate the uncertainty relations in two-qubit systems involving three physical components with the tight constant $2/sqrt3$. Our results provide a new insight into understanding the uncertainty relations with multiple observables and may motivate more innovative applications in quantum information science.
arXiv Detail & Related papers (2024-10-08T11:24:24Z)
Crossing exceptional points in non-Hermitian quantum systems [41.94295877935867]
We reveal the behavior of two-photon quantum states in non-Hermitian systems across the exceptional point. We demonstrate a switching in the quantum interference of photons directly at the exceptional point.
arXiv Detail & Related papers (2024-07-17T14:04:00Z)
Comparison of estimation limits for quantum two-parameter estimation [1.8507567676996612]
We compare the attainability of the Nagaoka Cram'er--Rao bound and the Lu--Wang uncertainty relation. We show that these two limits can provide different information about the physically attainable precision.
arXiv Detail & Related papers (2024-07-17T10:37:08Z)
Bayesian Logarithmic Derivative Type Lower Bounds for Quantum Estimation [17.305295658536828]
Recently, a lower bound, called the Bayesian Nagaoka-Hayashi bound for the Bayes risk in quantum domain was proposed. This paper is to explore this Bayesian Nagaoka-Hayashi bound further by obtaining its lower bounds.
arXiv Detail & Related papers (2024-05-17T04:07:16Z)
Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing [2.5449435573379757]
Quantum Cram'er-Rao bound is the ultimate limit of the mean squared error for unbiased estimation of an unknown parameter embedded in a quantum state. We apply our results to the cost of quantum-enhanced transmittance sensing.
arXiv Detail & Related papers (2024-02-27T22:28:42Z)
Error tradeoff relation for estimating the unitary-shift parameter of a relativistic spin-1/2 particle [20.44391436043906]
The purpose of this paper is to discuss the existence of a nontrivial tradeoff relation for estimating two unitary-shift parameters in a relativistic spin-1/2 system. It is shown that any moving observer cannot estimate two parameters simultaneously, even though a parametric model is classical in the rest frame.
arXiv Detail & Related papers (2023-08-01T17:07:29Z)
$\mathcal{PT}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities [0.0]
We present a new set of models with non-Hermiticity generated by splitting a Hermitian term into two Jordan-normal form parts. We find a robust PT threshold that seems insensitive to the size of the quantum spin chain.
arXiv Detail & Related papers (2023-04-20T03:03:58Z)
Uncertainty Relation for Non-Hermitian Systems [0.0]
We show that the cumulative gain in the quantum Fisher information when measuring two good observables for such non-Hermitian systems is way better than their Hermitian counterpart.
arXiv Detail & Related papers (2022-06-06T18:34:21Z)
Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
arXiv Detail & Related papers (2021-03-02T18:56:44Z)
The Quantum Wasserstein Distance of Order 1 [16.029406401970167]
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposed distance is invariant with respect to permutations of the qudits and unitary operations acting on one qudit. We also propose a generalization of the Lipschitz constant to quantum observables.
arXiv Detail & Related papers (2020-09-09T18:00:01Z)
Quantum enhanced metrology of Hamiltonian parameters beyond the Cram\`er-Rao bound [0.0]
This tutorial focuses on developments in quantum parameter estimation beyond the Cramer-Rao bound. It shows that an achievable bound to precision (beyond the Cramer-Rao) may be obtained in a closed form for the class of so-called controlled energy measurements.
arXiv Detail & Related papers (2020-03-05T08:35:40Z)

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