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Estimation under model misspecification arises in many signal processing problems, where the assumed observation model deviates from the true data-generating mechanism due to errors or simplifications. The misspecified Cram\'er-Rao bound…

Statistics Theory · Mathematics 2026-05-21 Malaak Khatib , Nadav Harel , Joseph Tabrikian , Tirza Routtenberg

The Cramer-Rao-Frechet inequality is reviewed specializing it to track fitting. A diffused opinion attributes to this inequality the limitation of the resolution of the track fits with the number N of observations. It turns out that this…

Instrumentation and Detectors · Physics 2021-10-22 Gregorio Landi , Giovanni E. Landi

Tight bounds on the minimum mean square error for the additive Gaussian noise channel are derived, when the input distribution is constrained to be epsilon-close to a Gaussian reference distribution in terms of the Kullback--Leibler…

Statistics Theory · Mathematics 2018-04-27 Michael Fauss , Alex Dytso , Abdelhak M. Zoubir , H. Vincent Poor

For a generic set of Markovian noise models, the estimation precision of a parameter associated with the Hamiltonian is limited by the $1/\sqrt{t}$ scaling where $t$ is the total probing time, in which case the maximal possible quantum…

Quantum Physics · Physics 2020-03-11 Sisi Zhou , Liang Jiang

In this paper, we derive for the first time the exact Cramer-Rao bounds (CRBs) on semi-blind channel estimation for amplify-and-forward two-way relay networks. The bounds cover a wide range of modulation schemes that satisfy a certain…

Information Theory · Computer Science 2012-07-24 Saeed Abdallah , Ioannis N. Psaromiligkos

We analyze the problem of estimating a signal from multiple measurements on a $\mbox{group action channel}$ that linearly transforms a signal by a random group action followed by a fixed projection and additive Gaussian noise. This channel…

Information Theory · Computer Science 2018-01-16 Emmanuel Abbe , João M. Pereira , Amit Singer

In this paper, an approximation recursive formula of the mean-square error lower bound for the discrete-time nonlinear filtering problem when noises of dynamic systems are temporally correlated is derived based on the Van Trees (posterior)…

Dynamical Systems · Mathematics 2015-04-28 Zhiguo Wang , Xiaojing Shen

Using a Bayesian methodology, we introduce the maximum a posteriori~(MAP) estimator for quantum state and process tomography. The maximum likelihood, hedged maximum likelihood, maximum likelihood-maximum entropy estimator, and estimators of…

Quantum Physics · Physics 2019-01-29 Vikesh Siddhu

We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…

Statistics Theory · Mathematics 2014-07-17 E. Ostrovsky , L. Sirota

In diffusion-based communication, as for molecular systems, the achievable data rate is very low due to the slow nature of diffusion and the existence of severe inter-symbol interference (ISI). Multiple-input multiple-output (MIMO)…

Information Theory · Computer Science 2018-01-23 S. Mohammadreza Rouzegar , Umberto Spagnolini

In the present study, time evolution of quantum Cramer-Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as…

Quantum Physics · Physics 2015-06-23 Farzam Nosraty

We investigate how squeezing techniques can improve the measurement precision in multiphase quantum metrology. While these methods are well-studied and effectively used in single-phase estimations, their usage in multiphase situations has…

Quantum Physics · Physics 2024-09-04 Le Bin Ho

The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…

Quantum Physics · Physics 2021-12-02 Jesús Rubio

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally…

Quantum Physics · Physics 2017-11-15 T. G. Downes , J. R. van Meter , E. Knill , G. J. Milburn , C. M. Caves

We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. It has recently been shown that, in the asymmetric setting with asymptotically vanishing type I error…

Quantum Physics · Physics 2024-03-28 Bjarne Bergh , Nilanjana Datta , Robert Salzmann , Mark M. Wilde

We propose two families of asymptotically local minimax lower bounds on parameter estimation performance. The first family of bounds applies to any convex, symmetric loss function that depends solely on the difference between the estimate…

Statistics Theory · Mathematics 2024-09-20 Neri Merhav

This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory,…

Information Theory · Computer Science 2025-01-23 Minhua Ding , Italo Atzeni , Antti Tölli , A. Lee Swindlehurst

In quantum computation, amplitude estimation is a fundamental subroutine that is utilized in various quantum algorithms. A general important task of such estimation problems is to characterize the estimation lower bound, which is referred…

Quantum Physics · Physics 2025-07-10 Kohei Oshio , Yohichi Suzuki , Kaito Wada , Keigo Hisanaga , Shumpei Uno , Naoki Yamamoto

In this letter, we analyse the properties of a maximum likelihood channel estimator based on the syndrome of a linear code. For the two examples of a binary symmetric channel and a binary input additive white Gaussian noise channel, we…

Information Theory · Computer Science 2013-12-12 Gottfried Lechner , Christoph Pacher

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show…

Quantum Physics · Physics 2022-11-23 Yakov Bloch , Eliahu Cohen