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We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…

Quantum Physics · Physics 2022-03-21 Daniel Uzcategui Contreras , Gabriel Senno , Dardo Goyeneche

We study the average case approximation of the Boolean mean by quantum algorithms. We prove general query lower bounds for classes of probability measures on the set of inputs. We pay special attention to two probabilities, where we show…

Quantum Physics · Physics 2007-05-23 A. Papageorgiou

The state estimation problem for nonlinear systems with stochastic uncertainties can be formulated in the Bayesian framework, where the objective is to replace the state completely by its probability density function. Without the…

Optimization and Control · Mathematics 2024-04-04 Lukas Ecker , Kurt Schlacher

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…

Machine Learning · Statistics 2020-12-15 Jarrad Courts , Johannes Hendriks , Adrian Wills , Thomas Schön , Brett Ninness

In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…

Numerical Analysis · Mathematics 2021-03-10 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…

Applications · Statistics 2017-04-17 Guillaume Bouleux , Rémy Boyer

Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the…

Quantum Physics · Physics 2021-10-20 Alex J. Belfield , Dorje C. Brody

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task.…

Quantum Physics · Physics 2023-09-12 Shoukang Chang , Wei Ye , Xuan Rao , Huan Zhang , Liqing Huang , Mengmeng Luo , Yuetao Chen , Qiang Ma , Shaoyan Gao

In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of…

Quantum Physics · Physics 2020-02-12 Xiao-Ming Lu , Zhihao Ma , Chengjie Zhang

We analyze the performance of a generalized Kitaev's phase estimation algorithm where N phase gates, acting on $M$ qubits prepared in a product state, may be distributed in an arbitrary way. Unlike the standard algorithm, where the mean…

Quantum Physics · Physics 2014-12-11 Tomasz Kaftal , Rafal Demkowicz-Dobrzanski

In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…

A generalization of the Gell-Mann-Low Theorem is applied to bound state calculations in Yukawa theory. The resulting effective Schroedinger equation is solved numerically for two-fermion bound states with the exchange of a massless boson.…

High Energy Physics - Phenomenology · Physics 2009-08-05 Axel Weber , Norbert E. Ligterink

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

Quantum Physics · Physics 2015-05-28 Tillmann Baumgratz , Martin B. Plenio

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…

Quantum Physics · Physics 2023-11-23 Jason L. Pereira , Leonardo Banchi , Stefano Pirandola

In quantum metrology, the Holevo Cram\'er-Rao bound has attracted renewed interest in recent years due to its superiority over the Helstrom Cram\'er-Rao bound and its asymptotic attainability for multi-parameter estimation. Its evaluation,…

Quantum Physics · Physics 2021-11-01 Mankei Tsang

Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…

Quantum Physics · Physics 2024-02-23 Valentin Gebhart , Manuel Gessner , Augusto Smerzi

-In this paper, we study Bayesian and hybrid Cramer-Rao bounds for the dynamical phase estimation of QAM modulated signals. We present the analytical expressions for the various CRBs. This avoids the calculation of any matrix inversion and…

Information Theory · Computer Science 2015-12-01 Jianxiao Yang , Benoit Geller , A Wei

Systems that are based on recursive Bayesian updates for classification limit the cost of evidence collection through certain stopping/termination criteria and accordingly enforce decision making. Conventionally, two termination criteria…

Machine Learning · Computer Science 2021-04-27 Aziz Kocanaogullari , Murat Akcakaya , Deniz Erdogmus

The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…

Quantum Physics · Physics 2015-12-09 Cristina Butucea , Madalin Guta , Theodore Kypraios

We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and…

Quantum Physics · Physics 2019-10-15 Sophie Schirmer , Frank Langbein