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Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as…

Information Theory · Computer Science 2016-08-24 Jens Steinwandt , Florian Roemer , Martin Haardt , Giovanni Del Galdo

We consider estimation of a single unknown parameter embedded in a quantum state. Quantum Cram\'er-Rao bound (QCRB) is the ultimate limit of the mean squared error for any unbiased estimator. While it can be achieved asymptotically for a…

Quantum Physics · Physics 2026-05-06 Zihao Gong , Boulat A. Bash

We calculate the Holevo Cram\'er-Rao bound for estimation of the displacement experienced by one mode of an two-mode squeezed vacuum state with squeezing r and find that it is equal to 4exp(-2r). This equals the sum of the mean squared…

Quantum Physics · Physics 2019-01-16 Mark Bradshaw , Syed M Assad , Ping Koy Lam

We consider the estimation of an unknown parameter $\theta$ through a quantum probe at thermal equilibrium. The probe is assumed to be in a Gibbs state according to its Hamiltonian $H_\theta$, which is divided in a parameter-encoding term…

Quantum Physics · Physics 2026-01-23 Paolo Abiuso , Pavel Sekatski , John Calsamiglia , Martí Perarnau-Llobet

The quantum Cram\'er-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same…

Quantum Physics · Physics 2025-03-21 J. Řeháček , J. L. Romero , A. Z. Goldberg , Z. Hradil , L. L. Sánchez-Soto

We investigate the problem of estimating simultaneously multiple parameters encoded in the shape of the modes on which the light is expanded. For this, we generalize the mode-encoded parameter estimation theory as introduced in Ref.[1] to a…

Quantum Physics · Physics 2025-05-23 Alexander Boeschoten , Giacomo Sorelli , Manuel Gessner , Claude Fabre , Nicolas Treps

We propose a quantum fitting scheme to estimate the magnetic field gradient with $N$-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. Our scheme combines the quantum multi-parameter estimation and the least…

Quantum Physics · Physics 2014-12-30 Yong-Liang Zhang , Huan Wang , Li Jing , Liang-Zhu Mu , Heng Fan

Mixed-resolution architectures, combining high-resolution (analog) data with coarsely quantized (e.g., 1-bit) data, are widely employed in emerging communication and radar systems to reduce hardware costs and power consumption. However, the…

Signal Processing · Electrical Eng. & Systems 2025-08-29 Yaniv Mazor , Tirza Routtenberg

The simultaneous estimation of multiple unknown parameters is the most general scenario in quantum sensing. Quantum multi-parameter estimation theory provides fundamental bounds on the achievable precision of simultaneous estimation.…

Quantum Physics · Physics 2025-12-02 Yaoling Yang , Victor Montenegro , Abolfazl Bayat

This paper focuses on radar waveform optimization for minimizing the Cram\'er-Rao bound (CRB) in a multiple-input multiple-output (MIMO) radar system. In contrast to conventional approaches relying on semi-definite programming (SDP) and…

Signal Processing · Electrical Eng. & Systems 2024-09-20 Xiaohua Zhou , Xu Du , Yijie Mao

In this paper, we derive the Cramer-Rao bound (CRB) for joint target position and velocity estimation using an active or passive distributed radar network under more general, and practically occurring, conditions than assumed in previous…

Statistics Theory · Mathematics 2016-04-20 Qian He , Jianbin Hu , Rick S. Blum , Yonggang Wu

This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…

Signal Processing · Electrical Eng. & Systems 2026-01-28 Heedong Do , Angel Lozano

In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known…

Quantum Physics · Physics 2023-08-30 Masahito Hayashi , Yingkai Ouyang

We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…

Quantum Physics · Physics 2023-10-11 Federico Girotti , Alfred Godley , Mădălin Guţă

The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…

Quantum Physics · Physics 2016-11-28 Paolo Giorda , Michele Allegra

Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements.…

Quantum Physics · Physics 2021-12-22 Bo-Fu Xie , Fei Ming , Dong Wang , Liu Ye , Jing-Ling Chen

We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…

Quantum Physics · Physics 2012-07-11 Vittorio Giovannetti , Seth Lloyd , Lorenzo Maccone

Recently, there is interest in coincident 'sharpening' and 'learnability' transitions in monitored quantum systems. In the latter, an outside observer's ability to infer properties of a quantum system from measurements undergoes a phase…

Statistical Mechanics · Physics 2025-04-15 Sun Woo P. Kim , Curt von Keyserlingk , Austen Lamacraft

The problem of estimating the parameters of a moving target in multiple-input multiple-output (MIMO) radar is considered and a new approach for estimating the moving target parameters by making use of the phase information associated with…

Information Theory · Computer Science 2015-06-04 Aboulnasr Hassanien , Sergiy A. Vorobyov , Alex B. Gershman

The Heisenberg limit provides a fundamental bound on the achievable estimation precision with a limited number of $N$ resources used (e.g., atoms, photons, etc.). Using entangled quantum states makes it possible to scale the precision with…

Quantum Physics · Physics 2023-04-28 Wojciech Górecki