Log in

Relevant bibliographies by topics / Quantum estimation theory / Journal articles

Journal articles on the topic 'Quantum estimation theory'

To see the other types of publications on this topic, follow the link: Quantum estimation theory.

Author: Grafiati

Published: 10 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Quantum estimation theory.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

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.

Full text

Abstract:

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 thoroughly review various schemes for estimating the phase of a qubit, identifying the underlying problem which prohibits these methods to reach the quantum Cramér-Rao bound, and propose a new adaptive scheme based on covariant measurements to circumvent this problem. Our findings are carefully checked by Monte Carlo simulations, showing that the method we propose is both mathematically and experimentally more realistic and more efficient than the methods currently available.

APA, Harvard, Vancouver, ISO, and other styles

2

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

Full text

Abstract:

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 the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The connections between the optmization procedure and the geometry of quantum statistical models are discussed. Our analysis allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices in quantum technology.

APA, Harvard, Vancouver, ISO, and other styles

3

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 (August 26, 2020): 385301. http://dx.doi.org/10.1088/1751-8121/aba770.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

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

Full text

Abstract:

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 model fed with experimental probabilities at a given evolution time. We compare our results with the bounds derived from estimation theory and find that the neural network acts as a nearly optimal estimator both when the estimation of two or three parameters is performed.

APA, Harvard, Vancouver, ISO, and other styles

5

Suzuki, Jun. "Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory." Entropy 21, no. 7 (July 18, 2019): 703. http://dx.doi.org/10.3390/e21070703.

Full text

Abstract:

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 quantum Fisher metrics and the properties of the tangent spaces of the quantum statistical model.

APA, Harvard, Vancouver, ISO, and other styles

6

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

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

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.

Full text

Abstract:

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 field in which Fock state, thermal state and coherent state are taken into account respectively. We calculate the quantum Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.

APA, Harvard, Vancouver, ISO, and other styles

8

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 (September 2017): 1750045. http://dx.doi.org/10.1142/s0219749917500459.

Full text

Abstract:

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 sensitivity to [Formula: see text]. We investigate how these quantifiers relate to the single-particle, mode entanglement in neutrino oscillations. We demonstrate that this form of entanglement does not enhance either of them. In particular, our results show that in single-particle settings, entanglement is not directly connected with the enhancement of precision in metrological tasks.

APA, Harvard, Vancouver, ISO, and other styles

9

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

10

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 (August 1, 2016): 13–39. http://dx.doi.org/10.1515/qmetro-2018-0002.

Full text

Abstract:

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 general precision bounds in the presence of an environment.We adopt a complementary approach,wherewe first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system’s dissipative time evolution.We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.

APA, Harvard, Vancouver, ISO, and other styles

11

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

Full text

Abstract:

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 make the quantum counting algorithm unbiased.

APA, Harvard, Vancouver, ISO, and other styles

12

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

13

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

Full text

Abstract:

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. However, the constant factor is large and thus the bound is loose. Our contribution in this paper is to provide the algorithm such that the upper bound of query complexity almost achieves the Heisenberg scaling and the constant factor is small.

APA, Harvard, Vancouver, ISO, and other styles

14

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

Full text

Abstract:

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 probabilities in the limit N → ∞. Finally, we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.

APA, Harvard, Vancouver, ISO, and other styles

15

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

16

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

Full text

Abstract:

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 vanishing with the deformation itself for all the considered classes of deformations and probe signals, thus making any estimation procedure of photon deformation inherently inefficient. A partial way out is provided by the polynomial dependence of the QSNR on the average number of photons, which suggests that, in principle, it would be possible to detect deformation by intensity measurements on high-energy thermal states.

APA, Harvard, Vancouver, ISO, and other styles

17

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

Full text

Abstract:

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 yields an asymptotic improvement in runtime, coming within a factor of $\log^*$ of the minimum number of measurements required while still requiring only minimal classical post-processing. The corresponding quantum circuit requires asymptotically lower depth and width (number of qubits) than quantum phase estimation.

APA, Harvard, Vancouver, ISO, and other styles

18

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 (February 2017): 1750009. http://dx.doi.org/10.1142/s0219749917500095.

Full text

Abstract:

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 calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation.

APA, Harvard, Vancouver, ISO, and other styles

19

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 (November 28, 2012): 5308–23. http://dx.doi.org/10.1098/rsta.2011.0528.

Full text

Abstract:

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 frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

APA, Harvard, Vancouver, ISO, and other styles

20

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

21

Arnhem, Matthieu, Evgueni Karpov, and Nicolas J. Cerf. "Optimal Estimation of Parameters Encoded in Quantum Coherent State Quadratures." Applied Sciences 9, no. 20 (October 11, 2019): 4264. http://dx.doi.org/10.3390/app9204264.

Full text

Abstract:

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 simultaneously.

APA, Harvard, Vancouver, ISO, and other styles

22

Spagnolo, Nicolò, Alessandro Lumino, Emanuele Polino, Adil S. Rab, Nathan Wiebe, and Fabio Sciarrino. "Machine Learning for Quantum Metrology." Proceedings 12, no. 1 (August 23, 2019): 28. http://dx.doi.org/10.3390/proceedings2019012028.

Full text

Abstract:

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 limited number of photons is employed.

APA, Harvard, Vancouver, ISO, and other styles

23

Cui, Xiaopeng, and Yu Shi. "Trotter errors in digital adiabatic quantum simulation of quantum ℤ2 lattice gauge theory." International Journal of Modern Physics B 34, no. 30 (August 19, 2020): 2050292. http://dx.doi.org/10.1142/s0217979220502926.

Full text

Abstract:

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 operators. They are much smaller than the order-of-magnitude estimation. The error in the symmetric decomposition is much smaller than that in the asymmetric decomposition. The features of the Trotter errors obtained here are useful in the experimental implementation of digital quantum simulation and its numerical demonstration.

APA, Harvard, Vancouver, ISO, and other styles

24

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 (January 2019): 1950028. http://dx.doi.org/10.1142/s0218271819500287.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

25

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

Full text

Abstract:

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 be useful for finding energy gaps in solid states.

APA, Harvard, Vancouver, ISO, and other styles

26

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

Full text

Abstract:

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 isomorphic to a Lie algebra of system operators from which one may approach the question of the existence of finite-dimensional filters.

APA, Harvard, Vancouver, ISO, and other styles

27

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

ELIZALDE, E., and S. D. ODINTSOV. "GRAVITATIONAL PHASE TRANSITIONS IN INFRARED QUANTUM GRAVITY." Modern Physics Letters A 08, no. 35 (November 20, 1993): 3325–33. http://dx.doi.org/10.1142/s0217732393003743.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

29

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

30

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

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

31

Suzuki, Jun. "Nuisance parameter problem in quantum estimation theory: tradeoff relation and qubit examples." Journal of Physics A: Mathematical and Theoretical 53, no. 26 (June 12, 2020): 264001. http://dx.doi.org/10.1088/1751-8121/ab8672.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Delgado, Francisco. "Symmetries of Quantum Fisher Information as Parameter Estimator for Pauli Channels under Indefinite Causal Order." Symmetry 14, no. 9 (September 1, 2022): 1813. http://dx.doi.org/10.3390/sym14091813.

Full text

Abstract:

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 Processing theories. For them, Pauli channels are an important family of parametric quantum channels providing the most faithful deformation effects of imperfect quantum communication channels. Recently, Pauli channels have been characterized when they are arranged in an Indefinite Causal Order. Thus, their fidelity has been compared with single or sequential arrangements of identical channels to analyse their induced transparency under a joint behaviour. The most recent characterization has exhibited important features for quantum communication related with their parametric nature. In this work, a parallel analysis has been conducted to extended such a characterization, this time in terms of their emerging Quantum Fisher Information to pursue the advantages of each kind of arrangement for the parameter estimation problem. The objective is to reach the arrangement stating the best estimation bound for each type of Pauli channel. A complete map for such an effectivity is provided for each Pauli channel under the most affordable setups considering sequential and Indefinite Causal Order arrangements, as well as discussing their advantages and disadvantages.

APA, Harvard, Vancouver, ISO, and other styles

33

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.

Full text

Abstract:

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 quantification of the Heisenberg squeezing bound for arbitrary estimation strategies that employ squeezing. Our theory recovers known results (e.g. in quantum optics and spin squeezing), but it uses the general theory of squeezing and holds for arbitrary quantum systems.

APA, Harvard, Vancouver, ISO, and other styles

34

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 (November 23, 2020): 1332. http://dx.doi.org/10.3390/e22111332.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

35

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

Full text

Abstract:

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 ratios based on the principles of quantum entanglement, and demonstrates that Bayes’ theorem is a special case of a more general quantum mechanical expression.

APA, Harvard, Vancouver, ISO, and other styles

36

Jizba, Petr, Jacob Dunningham, and Martin Prokš. "From Rényi Entropy Power to Information Scan of Quantum States." Entropy 23, no. 3 (March 12, 2021): 334. http://dx.doi.org/10.3390/e23030334.

Full text

Abstract:

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 can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.

APA, Harvard, Vancouver, ISO, and other styles

37

Wie, Chu-Ryang. "Simpler quantum counting." Quantum Information and Computation 19, no. 11&12 (September 2019): 967–83. http://dx.doi.org/10.26421/qic19.11-12-5.

Full text

Abstract:

A simpler quantum counting algorithm based on amplitude amplification is presented. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator where M is the number of marked states and N is the total number of states in the search space. This algorithm terminates within log(sqrt(N/M)) consecutive measurement steps when the probability p1 of measuring the state |1> is at least 0.5, and the result from the final step is used in estimating M by a classical post processing. The purpose of controlled-Grover iteration is to increase the probability p1. This algorithm requires less quantum resources in terms of the width and depth of the quantum circuit, produces a more accurate estimate of M, and runs significantly faster than the phase estimation-based quantum counting algorithm when the ratio M/N is small. We compare the two quantum counting algorithms by simulating various cases with a different M/N ratio, such as M/N > 0.125 or M/N < 0.001.

APA, Harvard, Vancouver, ISO, and other styles

38

Paris, Matteo G. A. "Quantum Binary Decision for Driven Harmonic Oscillator." International Journal of Modern Physics B 11, no. 29 (November 20, 1997): 3419–32. http://dx.doi.org/10.1142/s0217979297001684.

Full text

Abstract:

We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement scheme according to the Neyman–Pearson criterion. Detection probability has been evaluated for different initial state preparations of oscillator. The corresponding lower bounds on minimum detectable perturbation intensity has been evaluated and a general bound for random phase perturbation has been also induced.

APA, Harvard, Vancouver, ISO, and other styles

39

Takahira, Souichi, Asuka Ohashi, Tomohiro Sogabe, and Tsuyoshi S. Usuda. "Quantum algorithm for matrix functions by Cauchy's integral formula." Quantum Information and Computation 20, no. 1&2 (February 2020): 14–36. http://dx.doi.org/10.26421/qic20.1-2-2.

Full text

Abstract:

For matrix A, vector b and function f, the computation of vector f(A)b arises in many scientific computing applications. We consider the problem of obtaining quantum state |f> corresponding to vector f(A)b. There is a quantum algorithm to compute state |f> using eigenvalue estimation that uses phase estimation and Hamiltonian simulation e^{\im A t}. However, the algorithm based on eigenvalue estimation needs \poly(1/\epsilon) runtime, where \epsilon is the desired accuracy of the output state. Moreover, if matrix A is not Hermitian, \e^{\im A t} is not unitary and we cannot run eigenvalue estimation. In this paper, we propose a quantum algorithm that uses Cauchy's integral formula and the trapezoidal rule as an approach that avoids eigenvalue estimation. We show that the runtime of the algorithm is \poly(\log(1/\epsilon)) and the algorithm outputs state |f> even if A is not Hermitian.

APA, Harvard, Vancouver, ISO, and other styles

40

Maciel, Thiago O., and Reinaldo O. Vianna. "Optimal estimation of quantum processes using incomplete information: variational quantum process tomography." Quantum Information and Computation 12, no. 5&6 (May 2012): 442–47. http://dx.doi.org/10.26421/qic12.5-6-5.

Full text

Abstract:

We develop a quantum process tomography method, which variationally reconstruct the map of a process, using noisy and incomplete information about the dynamics. The new method encompasses the most common quantum process tomography schemes. It is based on the variational quantum tomography method (VQT) proposed by Maciel \emph{et al.} in arXiv:1001.1793[quant-ph] \cite{VQT}.

APA, Harvard, Vancouver, ISO, and other styles

41

Gomez, Ignacio S. "An Estimation of the Logarithmic Timescale in Ergodic Dynamics." International Journal of Bifurcation and Chaos 28, no. 01 (January 2018): 1850002. http://dx.doi.org/10.1142/s0218127418500025.

Full text

Abstract:

An estimation of the logarithmic timescale in quantum systems having an ergodic dynamics in the semiclassical limit, is presented. The estimation is based on an extension of the Krieger’s finite generator theorem for discretized [Formula: see text]-algebras and using the time rescaling property of the Kolmogorov–Sinai entropy. The results are in agreement with those obtained in the literature but with a simpler mathematics and within the context of the ergodic theory. Moreover, some consequences of the Poincaré’s recurrence theorem are also explored.

APA, Harvard, Vancouver, ISO, and other styles

42

Funada, Shin, and Jun Suzuki. "Uncertainty relation for estimating the position of an electron in a uniform magnetic field from quantum estimation theory." Physica A: Statistical Mechanics and its Applications 558 (November 2020): 124918. http://dx.doi.org/10.1016/j.physa.2020.124918.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Chowdhury and, Anirban Narayan, and Rolando D. Somma. "Quantum algorithms for Gibbs sampling and hitting-time estimation." Quantum Information and Computation 17, no. 1&2 (January 2017): 41–64. http://dx.doi.org/10.26421/qic17.1-2-3.

Full text

Abstract:

We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in p Nβ/Z and polynomial in log(1/epsilon), where N is the Hilbert space dimension, β is the inverse temperature, Z is the partition function, and epsilon is the desired precision of the output state. Our quantum algorithm exponentially improves the complexity dependence on 1/epsilon and polynomially improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix P, it runs in time almost linear in 1/(epsilon ∆3/2 ), where epsilon is the absolute precision in the estimation and ∆ is a parameter determined by P, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the complexity dependence on 1/epsilon and 1/∆ of the analog classical algorithm for hitting-time estimation. Both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.

APA, Harvard, Vancouver, ISO, and other styles

44

Luati, Alessandra, and Marco Novelli. "Explicit-duration Hidden Markov Models for quantum state estimation." Computational Statistics & Data Analysis 158 (June 2021): 107183. http://dx.doi.org/10.1016/j.csda.2021.107183.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Janzing, D., and T. Beth. "Quantum algorithm for measuring the eigenvalues of UÄU-1 for a black-box unitary transformation U." Quantum Information and Computation 2, no. 3 (April 2002): 192–97. http://dx.doi.org/10.26421/qic2.3-2.

Full text

Abstract:

Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure eigenvalues of U\otimesU^\deggar even in this case. Running the algorithm several times allows therefore to estimate the autocorrelation function of the density of eigenstates of U. This can be applied to find periodicities in the energy spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a quantum computer.

APA, Harvard, Vancouver, ISO, and other styles

46

Ahmadi, Hamed, and Chen-Fu Chiang. "Quantum phase estimation with arbitrary constant-precision phase shift operators." Quantum Information and Computation 12, no. 9&10 (September 2012): 864–75. http://dx.doi.org/10.26421/qic12.9-10-9.

Full text

Abstract:

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In this paper, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach.

APA, Harvard, Vancouver, ISO, and other styles

47

Jagielski, Adam, and Krzysztof Kanciak. "Grover on sparkle quantum resource estimation for a NIST LWC call finalist." Quantum Information and Computation 22, no. 13&14 (September 2022): 1132–43. http://dx.doi.org/10.26421/qic22.13-14-3.

Full text

Abstract:

In this paper, we propose an estimation of quantum resources necessary for recovering a key using Known Plain Text Attack (KPA) model for SPARKLE family of LWC authenticated block ciphers - SCHWAEMM. The procedure is based on a general attack using Grover's search algorithm with encryption oracle over key space in superposition. The paper explains step by step how to evaluate the cost of each operation type in encryption oracle in terms of various quantum and reversible gates. The result of this paper is an implementation of the simplified version of this cipher using quantum computer and summary table which shows the depth of quantum circuit, the size of quantum register and how many gates of NCT family are required for implementing the ciphers and attacks on them.

APA, Harvard, Vancouver, ISO, and other styles

48

Dai, Enze, Duan Huang, and Ling Zhang. "Low-Rate Denial-of-Service Attack Detection: Defense Strategy Based on Spectral Estimation for CV-QKD." Photonics 9, no. 6 (May 24, 2022): 365. http://dx.doi.org/10.3390/photonics9060365.

Full text

Abstract:

Although continuous-variable quantum key distribution (CVQKD) systems have unconditional security in theory, there are still many cyber attacking strategies proposed that exploit the loopholes of hardware devices and algorithms. At present, few studies have focused on attacks using algorithm vulnerabilities. The low-rate denial-of-service (LDoS) attack is precisely an algorithm-loophole based hacking strategy, which attacks by manipulating a channel’s transmittance T. In this paper, we take advantage of the feature that the power spectral density (PSD) of LDoS attacks in low frequency band is higher than normal traffic’s to detect whether there are LDoS attacks. We put forward a detection method based on the Bartlett spectral estimation approach and discuss its feasibility from two aspects, the estimation consistency and the detection accuracy. Our experiment results demonstrate that the method can effectively detect LDoS attacks and maintain the consistency of estimation. In addition, compared with the traditional method based on the wavelet transform and Hurst index estimations, our method has higher detection accuracy and stronger pertinence. We anticipate our method may provide an insight into how to detect an LDoS attack in a CVQKD system.

APA, Harvard, Vancouver, ISO, and other styles

49

Spekkens, R. W., and T. Rudolph. "Optimization of coherent attacks in generalizations of the BB84 quantum bit commitment protocol." Quantum Information and Computation 2, no. 1 (January 2002): 66–96. http://dx.doi.org/10.26421/qic2.1-4.

Full text

Abstract:

It is well known that no quantum bit commitment protocol is unconditionally secure. Nonetheless, there can be non-trivial upper bounds on both Bob's probability of correctly estimating Alice's commitment and Alice's probability of successfully unveiling whatever bit she desires. In this paper, we seek to determine these bounds for generalizations of the BB84 bit commitment protocol. In such protocols, an honest Alice commits to a bit by randomly choosing a state from a specified set and submitting this to Bob, and later unveils the bit to Bob by announcing the chosen state, at which point Bob measures the projector onto the state. Bob's optimal cheating strategy can be easily deduced from well known results in the theory of quantum state estimation. We show how to understand Alice's most general cheating strategy, (which involves her submitting to Bob one half of an entangled state) in terms of a theorem of Hughston, Jozsa and Wootters. We also show how the problem of optimizing Alice's cheating strategy for a fixed submitted state can be mapped onto a problem of state estimation. Finally, using the Bloch ball representation of qubit states, we identify the optimal coherent attack for a class of protocols that can be implemented with just a single qubit. These results provide a tight upper bound on Alice's probability of successfully unveiling whatever bit she desires in the protocol proposed by Aharonov et al., and lead us to identify a qubit protocol with even greater security.

APA, Harvard, Vancouver, ISO, and other styles

50

Prettico, Giuseppe, and Antonio Acin. "Can bipartite classical information resources be activated?" Quantum Information and Computation 13, no. 3&4 (March 2013): 245–65. http://dx.doi.org/10.26421/qic13.3-4-6.

Full text

Abstract:

Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a secret key. Exploiting the analogies between the entanglement and the secret-key agreement scenario, we provide some evidence that the secret-key rate may be a non-additive quantity. In particular, we show that correlations with conjectured bound information become secret-key distillable when combined. Our results constitute a new instance of the subtle relation between the entanglement and secret-key agreement scenario.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!