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Articles de revues sur le sujet « Quantum estimation theory »

Auteur : Grafiati

Publié le 10 mars 2023

Mis à jour le 26 juillet 2025

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1

Rodríguez-García, Marco A., Isaac Pérez Castillo, and P. Barberis-Blostein. "Efficient qubit phase estimation using adaptive measurements." Quantum 5 (June 4, 2021): 467. http://dx.doi.org/10.22331/q-2021-06-04-467.

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Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is given by the so-called quantum Cramér-Rao bound, so any measurement strategy aims to obtain estimations as close as possible to it. However, more often than not, the current state-of-the-art methods to estimate quantum phases fail to reach this bound as they rely on maximum likelihood estimators of non-identifiable likelihood functions. In this work we thoro

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Alexei, Kaltchenko. "Estimation of quantum entropies." i-manager’s Journal on Mathematics 13, no. 1 (2024): 1. http://dx.doi.org/10.26634/jmat.13.1.20387.

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Motivated by the importance of entropy functions in quantum data compression, entanglement theory, and various quantum information-processing tasks, this study demonstrates how classical algorithms for entropy estimation can effectively contribute to the construction of quantum algorithms for universal quantum entropy estimation. Given two quantum i.i.d. sources with completely unknown density matrices, algorithms are developed for estimating quantum cross entropy and quantum relative entropy. These estimation techniques represent a quantum generalization of the classical algorithms by Lempel,

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Khalesi, Elham. "Quantum Theory Proof Show by MATLAB Software." Journal of Applied Material Science & Engineering Research 7, no. 2 (2023): 107–8. https://doi.org/10.33140/jamser.07.02.04.

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This paper is based on Numeric Estimation that for unsymmetrical figures has benefits. Also, this project by Finite Difference Method and Matlab Programming and knowing potential in boundary condition , field in Microwave Devices or parameters in Transfer Electronics Line obtain.

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Marchese, Marta Maria, Alessio Belenchia, and Mauro Paternostro. "Optomechanics-Based Quantum Estimation Theory for Collapse Models." Entropy 25, no. 3 (2023): 500. http://dx.doi.org/10.3390/e25030500.

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We make use of the powerful formalism of quantum parameter estimation to assess the characteristic rates of a continuous spontaneous localization (CSL) model affecting the motion of a massive mechanical system. We show that a study performed in non-equilibrium conditions unveils the advantages provided by the use of genuinely quantum resources—such as quantum correlations—in estimating the CSL-induced diffusion rate. In stationary conditions, instead, the gap between quantum performance and a classical scheme disappears. Our investigation contributes to the ongoing effort aimed at identifying

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PARIS, MATTEO G. A. "QUANTUM ESTIMATION FOR QUANTUM TECHNOLOGY." International Journal of Quantum Information 07, supp01 (2009): 125–37. http://dx.doi.org/10.1142/s0219749909004839.

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Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e. the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and th

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Bakmou, Lahcen, Mohammed Daoud, and Rachid ahl laamara. "Multiparameter quantum estimation theory in quantum Gaussian states." Journal of Physics A: Mathematical and Theoretical 53, no. 38 (2020): 385301. http://dx.doi.org/10.1088/1751-8121/aba770.

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Wada, Kaito, Kazuma Fukuchi, and Naoki Yamamoto. "Quantum-enhanced mean value estimation via adaptive measurement." Quantum 8 (September 9, 2024): 1463. http://dx.doi.org/10.22331/q-2024-09-09-1463.

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Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cramér-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is hi

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Gianani, Ilaria, and Claudia Benedetti. "Multiparameter estimation of continuous-time quantum walk Hamiltonians through machine learning." AVS Quantum Science 5, no. 1 (2023): 014405. http://dx.doi.org/10.1116/5.0137398.

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The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum walks, the parameters themselves may not be directly accessible, and, thus, it is necessary to find alternative estimation strategies exploiting other observables. Here, we perform the multiparameter estimation of the Hamiltonian parameters characterizing a continuous-time quantum walk over a line graph with n-neighbor interactions using a deep neural network mod

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Hayashi, Masahito, and Yingkai Ouyang. "The Cramér-Rao approach and global quantum estimation of bosonic states." Quantum 9 (July 22, 2025): 1806. https://doi.org/10.22331/q-2025-07-22-1806.

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Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cramér Rao approach which considers local estimation gives the ultimate precision bound of quantum state estimation in terms of the quantum Fisher information. However practical scenarios need not offer much prior information about the parameters to be estimated, and the local estimation setting need not apply. In general, it is unclear whether the Cramér-Rao approach is

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Suzuki, Jun. "Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory." Entropy 21, no. 7 (2019): 703. http://dx.doi.org/10.3390/e21070703.

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In this paper, we classify quantum statistical models based on their information geometric properties and the estimation error bound, known as the Holevo bound, into four different classes: classical, quasi-classical, D-invariant, and asymptotically classical models. We then characterize each model by several equivalent conditions and discuss their properties. This result enables us to explore the relationships among these four models as well as reveals the geometrical understanding of quantum statistical models. In particular, we show that each class of model can be identified by comparing qu

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Niu, Ming-Li, Yue-Ming Wang, and Zhi-Jian Li. "Estimation of light-matter coupling constant under dispersive interaction based on quantum Fisher information." Acta Physica Sinica 71, no. 9 (2022): 090601. http://dx.doi.org/10.7498/aps.71.20212029.

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Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation－quantum Cramer-Rao bound－shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. The initial probing state is the direct product state of qubit and radiation fiel

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Kent, Adrian. "The measurement postulates of quantum mechanics are not redundant." Quantum 9 (May 20, 2025): 1749. https://doi.org/10.22331/q-2025-05-20-1749.

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Masanes, Galley and Müller \cite{masanes2019measurement} argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates together with an assumption they call the "possibility of state estimation". Their argument also relies on what they term a "theory-independent characterization of measurements for single and multipartite systems". We refute their conclusion, giving explicit examples of non-quantum measurement and state update rules that satisfy all their assumptions. We also show that their "possibility of state estimation" assumption is nei

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Fujiwara, A. "Statistical estimation of a quantum operation." Quantum Information and Computation 4, no. 6&7 (2004): 479–88. http://dx.doi.org/10.26421/qic4.6-7-7.

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Tsang, Mankei. "Operational meanings of a generalized conditional expectation in quantum metrology." Quantum 7 (November 3, 2023): 1162. http://dx.doi.org/10.22331/q-2023-11-03-1162.

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A unifying formalism of generalized conditional expectations (GCEs) for quantum mechanics has recently emerged, but its physical implications regarding the retrodiction of a quantum observable remain controversial. To address the controversy, here I offer operational meanings for a version of the GCEs in the context of quantum parameter estimation. When a quantum sensor is corrupted by decoherence, the GCE is found to relate the operator-valued optimal estimators before and after the decoherence. Furthermore, the error increase, or regret, caused by the decoherence is shown to be equal to a di

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Haase, J. F., A. Smirne, S. F. Huelga, J. Kołodynski, and R. Demkowicz-Dobrzanski. "Precision Limits in Quantum Metrology with Open Quantum Systems." Quantum Measurements and Quantum Metrology 5, no. 1 (2016): 13–39. http://dx.doi.org/10.1515/qmetro-2018-0002.

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Abstract The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcomewhen using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining gen

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Nogueira, Edson C., Gustavo de Souza, Adalberto D. Varizi, and Marcos D. Sampaio. "Quantum estimation in neutrino oscillations." International Journal of Quantum Information 15, no. 06 (2017): 1750045. http://dx.doi.org/10.1142/s0219749917500459.

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In this work, we analyze two-flavor neutrino oscillations within the framework of quantum estimation theory (QET). We compute the quantum Fischer information (QFI) for the mixing angle [Formula: see text] and show that mass measurements are the ones that achieve optimal precision. We also study the Fischer information (FI) associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sens

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JARVIS, P. D., and J. G. SUMNER. "ADVENTURES IN INVARIANT THEORY." ANZIAM Journal 56, no. 2 (2014): 105–15. http://dx.doi.org/10.1017/s1446181114000327.

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AbstractWe provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualized via two case studies, arising from our recent work: entanglement invariants for characterizing the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics.

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Streater, R. F. "Proof of a Modified Jaynes's Estimation Theory." Open Systems & Information Dynamics 18, no. 02 (2011): 223–33. http://dx.doi.org/10.1142/s1230161211000157.

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It is proved that the state of maximum entropy, having observed values for the n observables, X1,…,Xn, is the same state that minimises the matrix of covariances of any n locally unbiased estimators for n parameters for the probability distribution of X1,…,Xn. We sketch how to get a similar result in quantum theory, in which X1,…,Xn are (not necessarily commuting) quadratic forms that are bounded relative to a positive self-adjoint operator H such that exp (-βH) is of trace-class for some positive β.

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Drucker, Andrew, and Ronald de Wolf. "Uniform approximation by (quantum) polynomials." Quantum Information and Computation 11, no. 3&4 (2011): 215–25. http://dx.doi.org/10.26421/qic11.3-4-2.

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We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectively on quantum counting and on quantum phase estimation.

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Cătană, Cătălin, Merlijn van Horssen, and Mădălin Guţă. "Asymptotic inference in system identification for the atom maser." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (2012): 5308–23. http://dx.doi.org/10.1098/rsta.2011.0528.

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System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi freq

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Nakaji, Kouhei. "Faster amplitude estimation." Quantum Information and Computation 20, no. 13&14 (2020): 1109–23. http://dx.doi.org/10.26421/qic20.13-14-2.

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In this paper, we introduce an efficient algorithm for the quantum amplitude estimation task which is tailored for near-term quantum computers. The quantum amplitude estimation is an important problem which has various applications in fields such as quantum chemistry, machine learning, and finance. Because the well-known algorithm for the quantum amplitude estimation using the phase estimation does not work in near-term quantum computers, alternative approaches have been proposed in recent literature. Some of them provide a proof of the upper bound which almost achieves the Heisenberg scaling.

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Mitarai, Kosuke, Kiichiro Toyoizumi, and Wataru Mizukami. "Perturbation theory with quantum signal processing." Quantum 7 (May 12, 2023): 1000. http://dx.doi.org/10.22331/q-2023-05-12-1000.

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Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on quantum computers. The benefit of using quantum computers is that we can start the perturbation from a Hamiltonian that is classically hard to solve. The proposed algorithm uses quantum signal processing (QSP) to achieve this goal. Along with the perturbation theory, we construct a technique for ground state preparation with detailed computational cost analysi

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KEYL, M. "QUANTUM STATE ESTIMATION AND LARGE DEVIATIONS." Reviews in Mathematical Physics 18, no. 01 (2006): 19–60. http://dx.doi.org/10.1142/s0129055x06002565.

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In this paper we propose a method to estimate the density matrix ρ of a d-level quantum system by measurements on the N-fold system in the joint state ρ⊗N. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning pure states and the estimation of the spectrum of ρ. We show that it is consistent (i.e. the original input state ρ is recovered with certainty if N → ∞), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilitie

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Lu, Xi, and Hongwei Lin. "Unbiased quantum phase estimation." Quantum Information and Computation 23, no. 1&2 (2023): 16–26. http://dx.doi.org/10.26421/qic23.1-2-2.

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Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. However, we find that the PEA is not an unbiased estimation, which prevents the estimation error from achieving an arbitrarily small level. In this paper, we propose an unbiased phase estimation algorithm (UPEA) based on the original PEA. We also show that a maximum likelihood estimation (MLE) post-processing step applied on UPEA has a smaller mean absolute error than MLE applied on PEA. In the end, we apply UPEA to quantum counting, and use an additional correction step to

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Assad, Syed M., Mark Bradshaw, and Ping Koy Lam. "Phase estimation of coherent states with a noiseless linear amplifier." International Journal of Quantum Information 15, no. 01 (2017): 1750009. http://dx.doi.org/10.1142/s0219749917500095.

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Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still be possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calc

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De Cillis, Giovanni, and Matteo G. A. Paris. "Quantum limits to estimation of photon deformation." International Journal of Quantum Information 12, no. 02 (2014): 1461009. http://dx.doi.org/10.1142/s0219749914610097.

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We address potential deviations of radiation field from the bosonic behavior and employ local quantum estimation theory to evaluate the ultimate bounds to precision in the estimation of these deviations using quantum-limited measurements on optical signals. We consider different classes of boson deformations and found that intensity measurement on coherent or thermal states would be suitable for their detection making, at least in principle, tests of boson deformation feasible with current quantum optical technology. On the other hand, we found that the quantum signal-to-noise ratio (QSNR) is

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Demkowicz-Dobrzański, Rafał. "Pomiary kwantowe A.D. 2023." Postępy Fizyki 74, no. 2 (2023): 13–18. http://dx.doi.org/10.61947/uw.pf.2023.74.2.13-18.

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In the article a quantum estimation theory perspective on the concept of quantum measurement is presented, as well as the latest theoretical and experimental developments in the field of quantum metrology, with particular focus on the contribution of a research group from the University of Warsaw to the development of theoretical methods.

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Svore, Krysta M., Matthew B. Hastings, and Michael Freedman. "Faster phase estimation." Quantum Information and Computation 14, no. 3&4 (2014): 306–28. http://dx.doi.org/10.26421/qic14.3-4-7.

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We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width. We show that the use of purely random measurements requires a number of measurements that is optimal up to constant factors, albeit at the cost of exponential classical post-processing; the method can also be used to improve classical signal processing. We then develop a quantum algorithm for phase estimation that yie

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YAMAGATA, KOICHI. "EFFICIENCY OF QUANTUM STATE TOMOGRAPHY FOR QUBITS." International Journal of Quantum Information 09, no. 04 (2011): 1167–83. http://dx.doi.org/10.1142/s0219749911007551.

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The efficiency of quantum state tomography is discussed from the point of view of quantum parameter estimation theory, in which the trace of the weighted covariance is to be minimized. It is shown that tomography is optimal only when a special weight is adopted.

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Arnhem, Matthieu, Evgueni Karpov, and Nicolas J. Cerf. "Optimal Estimation of Parameters Encoded in Quantum Coherent State Quadratures." Applied Sciences 9, no. 20 (2019): 4264. http://dx.doi.org/10.3390/app9204264.

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In the context of multiparameter quantum estimation theory, we investigate the construction of linear schemes in order to infer two classical parameters that are encoded in the quadratures of two quantum coherent states. The optimality of the scheme built on two phase-conjugate coherent states is proven with the saturation of the quantum Cramér–Rao bound under some global energy constraint. In a more general setting, we consider and analyze a variety of n-mode schemes that can be used to encode n classical parameters into n quantum coherent states and then estimate all parameters optimally and

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Spagnolo, Nicolò, Alessandro Lumino, Emanuele Polino, Adil S. Rab, Nathan Wiebe, and Fabio Sciarrino. "Machine Learning for Quantum Metrology." Proceedings 12, no. 1 (2019): 28. http://dx.doi.org/10.3390/proceedings2019012028.

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Phase estimation represents a significant example to test the application of quantum theory for enhanced measurements of unknown physical parameters. Several recipes have been developed, allowing to define strategies to reach the ultimate bounds in the asymptotic limit of a large number of trials. However, in certain applications it is crucial to reach such bound when only a small number of probes is employed. Here, we discuss an asymptotically optimal, machine learning based, adaptive single-photon phase estimation protocol that allows us to reach the standard quantum limit when a very limite

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Sinanan-Singh, Jasmine, Gabriel L. Mintzer, Isaac L. Chuang, and Yuan Liu. "Single-shot Quantum Signal Processing Interferometry." Quantum 8 (July 30, 2024): 1427. http://dx.doi.org/10.22331/q-2024-07-30-1427.

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Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator&apos;s quadrature operators by generalizing quantum signal proce

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Janzing, D. "Quantum algorithm for measuring the energy of n qubits with unknown pair-interactions." Quantum Information and Computation 2, no. 3 (2002): 198–207. http://dx.doi.org/10.26421/qic2.3-3.

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The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown n-qubit pair-interaction Hamiltonian into a conditional one such that standard phase estimation can be applied to measure the energy. Our essential assumption is that the considered system can be brought into interaction with a quantum computer. For large n the algorithm could still be applicable for estimating the density of energy states and might therefore b

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Costa, H. A. S., P. R. S. Carvalho, and I. G. da Paz. "Parameter estimation for a Lorentz invariance violation." International Journal of Modern Physics D 28, no. 01 (2019): 1950028. http://dx.doi.org/10.1142/s0218271819500287.

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We employ techniques from quantum estimation theory (QET) to estimate the Lorentz violation parameters in the (1+3)-dimensional flat spacetime. We obtain and discuss the expression of the quantum Fisher information (QFI) in terms of the Lorentz violation parameter [Formula: see text] and the momentum [Formula: see text] of the created particles. We show that the maximum QFI is achieved for a specific momentum [Formula: see text]. We also find that the optimal precision of estimation of the Lorentz violation parameter is obtained near the Planck scale.

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MUÑOZ-TAPIA, R., J. TARON, and R. TARRACH. "THE UNCERTAINTY OF THE GAUSSIAN EFFECTIVE POTENTIAL." International Journal of Modern Physics A 03, no. 09 (1988): 2143–63. http://dx.doi.org/10.1142/s0217751x88000898.

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An uncertainty is introduced for the Gaussian Effective Potential. The definition is quite straightforward for quantum mechanics but fairly subtle for quantum field theory. The uncertainty provides a good estimation of the error in the first case, but renormalization seems to spoil its usefulness in the second case. The examples considered are the anharmonic oscillator, λϕ4 in 3+1 dimensions and the Liouville theory in 1+1 dimensions.

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Ojima, Izumi, and Kazuya Okamura. "Large Deviation Strategy for Inverse Problem II." Open Systems & Information Dynamics 19, no. 03 (2012): 1250022. http://dx.doi.org/10.1142/s1230161212500229.

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In the earlier paper [1], we have proposed the large deviation strategy (LDS) and discussed its first level. By efficient use of the central measure, we will establish a quantum version of Sanov's theorem, the Bayesian escort predictive state and the widely applicable information criteria for quantum states in LDS second level. Finally, these results are re-examined in the context of quantum estimation theory, and organized as quantum model selection, i.e., a quantum version of model selection.

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ELIZALDE, E., and S. D. ODINTSOV. "GRAVITATIONAL PHASE TRANSITIONS IN INFRARED QUANTUM GRAVITY." Modern Physics Letters A 08, no. 35 (1993): 3325–33. http://dx.doi.org/10.1142/s0217732393003743.

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The conformal anomaly induced sector of four-dimensional quantum gravity (ir quantum gravity), which has been introduced by Antoniadis and Mottola, is studied here on a curved fiducial background. The one-loop effective potential for the effective conformal factor theory is calculated with accuracy, including terms linear in the curvature. It is proved that a curvature induced phase transition can actually take place. An estimation of the critical curvature for different choices of the parameters of the theory is given.

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Cui, Xiaopeng, та Yu Shi. "Trotter errors in digital adiabatic quantum simulation of quantum ℤ2 lattice gauge theory". International Journal of Modern Physics B 34, № 30 (2020): 2050292. http://dx.doi.org/10.1142/s0217979220502926.

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Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of (2[Formula: see text]+[Formula: see text]1)-dimensional quantum [Formula: see text] lattice gauge theory. The actual errors in Trotter decompositions are investigated as functions of the coupling parameter and the number of Trotter substeps in each step of the variation of coupling parameter. The relative error of energy is shown to be equal to the Trotter error usually defined in terms of the evolution o

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Chakrabarti, Shouvanik, Andrew M. Childs, Shih-Han Hung, Tongyang Li, Chunhao Wang, and Xiaodi Wu. "Quantum Algorithm for Estimating Volumes of Convex Bodies." ACM Transactions on Quantum Computing 4, no. 3 (2023): 1–60. http://dx.doi.org/10.1145/3588579.

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Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an n -dimensional convex body within multiplicative error ε using Õ(n 3 + n 2.5 /ε ) queries to a membership oracle and Õ(n 5 +n 4.5 /ε) additional arithmetic operations. For comparison, the best known classical algorithm uses Õ(n 3.5 +n 3 /ε 2 ) queries and Õ(n 5.5 +n 5 /ε 2 ) additional arithmetic operations. To the best of our knowledge, this is the first quantum speedup for volume estimation. Ou

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Amini, Nina H., and John E. Gough. "The Estimation Lie Algebra Associated with Quantum Filters." Open Systems & Information Dynamics 26, no. 02 (2019): 1950004. http://dx.doi.org/10.1142/s1230161219500045.

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We introduce the Lie algebra of super-operators associated with a quantum filter, specifically emerging from the Stratonovich calculus. In classical filtering, the analogue algebra leads to a geometric theory of nonlinear filtering which leads to well-known results by Brockett and by Mitter characterizing potential models where the curse-of-dimensionality may be avoided, and finite dimensional filters obtained. We discuss the quantum analogue to these results. In particular, we see that, in the case where all outputs are subjected to homodyne measurement, the Lie algebra of super-operators is

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Barman, Himangshu, and Palash Mandal. "Estimation of Correction of Ground State Energy of Hydrogen Atom in Presence of Quadratic GUP." International Journal for Research in Applied Science and Engineering Technology 11, no. 6 (2023): 3393–95. http://dx.doi.org/10.22214/ijraset.2023.54315.

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Abstract: String Theory, Quantum Geometry, Loop Quantum Gravity and Black Hole physic all predict the existence of a observable minimal length at Planck scale. For example, in case of string theory it is conjectured that a particle described as a string does not interact at distances smaller than its size. As a consequence, the HUP has to be generalized to take into account this aspect. The models which are designed to implement the minimal length scale and/or the maximum momentum in different physical systems entered into the literature as the Generalized Uncertainty Principle (GUP). Here, qu

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Chantasri, Areeya, Ivonne Guevara, Kiarn T. Laverick, and Howard M. Wiseman. "Unifying theory of quantum state estimation using past and future information." Physics Reports 930 (October 2021): 1–40. http://dx.doi.org/10.1016/j.physrep.2021.07.003.

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Maccone, Lorenzo, and Alberto Riccardi. "Squeezing metrology: a unified framework." Quantum 4 (July 9, 2020): 292. http://dx.doi.org/10.22331/q-2020-07-09-292.

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Quantum metrology theory has up to now focused on the resolution gains obtainable thanks to the entanglement among N probes. Typically, a quadratic gain in resolution is achievable, going from the 1/N of the central limit theorem to the 1/N of the Heisenberg bound. Here we focus instead on quantum squeezing and provide a unified framework for metrology with squeezing, showing that, similarly, one can generally attain a quadratic gain when comparing the resolution achievable by a squeezed probe to the best N-probe classical strategy achievable with the same energy. Namely, here we give a quanti

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Shen, Yizhi, Katherine Klymko, James Sud, David B. Williams-Young, Wibe A. de Jong, and Norm M. Tubman. "Real-Time Krylov Theory for Quantum Computing Algorithms." Quantum 7 (July 25, 2023): 1066. http://dx.doi.org/10.22331/q-2023-07-25-1066.

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Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalize

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Delgado, Francisco. "Symmetries of Quantum Fisher Information as Parameter Estimator for Pauli Channels under Indefinite Causal Order." Symmetry 14, no. 9 (2022): 1813. http://dx.doi.org/10.3390/sym14091813.

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Quantum Fisher Information is considered in Quantum Information literature as the main resource to determine a bound in the parametric characterization problem of a quantum channel by means of probe states. The parameters characterizing a quantum channel can be estimated until a limited precision settled by the Cramér–Rao bound established in estimation theory and statistics. The involved Quantum Fisher Information of the emerging quantum state provides such a bound. Quantum states with dimension d=2, the qubits, still comprise the main resources considered in Quantum Information and Quantum P

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Bond, Rachael L., Yang-Hui He, and Thomas C. Ormerod. "A quantum framework for likelihood ratios." International Journal of Quantum Information 16, no. 01 (2018): 1850002. http://dx.doi.org/10.1142/s0219749918500028.

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The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes’ theorem either defaults to the marginal probability driven “naive Bayes’ classifier”, or requires the use of compensatory expectation-maximization techniques. This paper takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood

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Jizba, Petr, Jacob Dunningham, and Martin Prokš. "From Rényi Entropy Power to Information Scan of Quantum States." Entropy 23, no. 3 (2021): 334. http://dx.doi.org/10.3390/e23030334.

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In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state

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Markovich, Liubov A., Justus Urbanetz, and Vladimir I. Man’ko. "Not All Probability Density Functions Are Tomograms." Entropy 26, no. 3 (2024): 176. http://dx.doi.org/10.3390/e26030176.

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This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful whe

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Suzuki, Jun. "Nuisance parameter problem in quantum estimation theory: tradeoff relation and qubit examples." Journal of Physics A: Mathematical and Theoretical 53, no. 26 (2020): 264001. http://dx.doi.org/10.1088/1751-8121/ab8672.

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Ciaglia, Florio M., Jürgen Jost, and Lorenz Schwachhöfer. "Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras." Entropy 22, no. 11 (2020): 1332. http://dx.doi.org/10.3390/e22111332.

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A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.

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