scholarly journals A SIMPLE MINIMAX ESTIMATOR FOR QUANTUM STATES

2012 ◽  
Vol 10 (04) ◽  
pp. 1250038 ◽  
Author(s):  
HUI KHOON NG ◽  
BERTHOLD-GEORG ENGLERT
Keyword(s):  
Quantum Information Processing ◽  
Full Rank ◽  
Quantum Tomography ◽  
The State ◽  
Repeated Measurements ◽  
Quantum States ◽  
Data Sets ◽  
Minimax Estimator ◽  
Technological Challenge ◽  
Ml Estimator

Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting the gathered data into an estimate of the state works very well. For smaller data sets, however, it often suffers from problems of rank deficiency in the estimated state. For many systems of relevance for quantum information processing, the preparation of a very large number of copies of the same quantum state is still a technological challenge, which motivates us to look for estimation strategies that perform well even when there is not much data. After reviewing the concept of minimax state estimation, we use minimax ideas to construct a simple estimator for quantum states. We demonstrate that, for the case of tomography of a single qubit, our estimator significantly outperforms the ML estimator for small number of copies of the state measured. Our estimator is always full-rank, and furthermore, has a natural dependence on the number of copies measured, which is missing in the ML estimator.

scholarly journals Purification and redistribution of entanglement via single local filtering

2014 ◽  
Vol 12 (01) ◽  
pp. 1450004 ◽  
Author(s):  
K. O. Yashodamma ◽  
P. J. Geetha ◽  
Sudha
Keyword(s):  
Quantum State ◽  
The State ◽  
Quantum States ◽  
Local Action ◽  
Entanglement Transfer ◽  
Local Filtering

The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the composite quantum state allows for purification of the remaining part of the state. The redistribution of entanglement in the subsystems of a noise affected state is shown to be due to the action of local filtering on the non-decohering part of the system. The varying effects of the filtering parameter, on the entanglement transfer between the subsystems, depending on the choice of the initial quantum state is illustrated.

Belief Movement, Uncertainty Reduction, and Rational Updating*

2021 ◽  
Author(s):  
Ned Augenblick ◽  
Matthew Rabin
Keyword(s):  
Statistical Tests ◽  
Uncertainty Reduction ◽  
The State ◽  
Data Sets ◽  
New Information ◽  
The World ◽  
Core Concepts ◽  
Market Beliefs ◽  
Over Time

Abstract When a Bayesian learns new information and changes her beliefs, she must on average become concomitantly more certain about the state of the world. Consequently, it is rare for a Bayesian to frequently shift beliefs substantially while remaining relatively uncertain, or, conversely, become very confident with relatively little belief movement. We formalize this intuition by developing specific measures of movement and uncertainty reduction given a Bayesian’s changing beliefs over time, showing that these measures are equal in expectation and creating consequent statistical tests for Bayesianess. We then show connections between these two core concepts and four common psychological biases, suggesting that the test might be particularly good at detecting these biases. We provide support for this conclusion by simulating the performance of our test and other martingale tests. Finally, we apply our test to data sets of individual, algorithmic, and market beliefs.

scholarly journals EVALUATION OF THE INFLUENCE OF SOCIAL AND ECONOMIC DETERMINANTS ON THE STATE OF PUBLIC HEALTH ON THE BASIS OF MICROIMITATION MODELING

2017 ◽  
pp. 79-90
Author(s):  
Dmytro Shushpanov ◽  
Volodymyr Sarioglo
Keyword(s):  
Research Policy ◽  
Synthetic Data ◽  
Simulation Models ◽  
The State ◽  
Data Sets ◽  
Economic Determinants ◽  
Micro Simulation ◽  
State Employment ◽  
Health Research Policy ◽  
Main Determinants

In the article the essence and peculiarities of microimitational modeling are considered. The advantages of microimitational models over the statistics models are substantiated. Micro-simulation models, that prognosticate somehow dynamic changes in health and which are most appropriate to use in development and health research policy, such as POHEM, CORSIM and Sife Paths, are outlined. It is proposed to use elements of statistical and dynamic microimitation modeling, agent modeling and the concept of a life course for the estimation of the influence social and economic determinants. The synthetic model of population which has been formed on the basis of representative data sets of sample surveys of living conditions of households and economic activity of the population of the State Employment Service of Ukraine, as well as microdata of the Multicultural Survey of the Population of Ukraine (2012) and the Medical and Demographic Survey (2013). The generalized scheme of the method of microimulation modeling of the influence of social and economic determinants on the health status of the population of Ukraine has been developed. The influence of the main determinants on the health of certain age, gender and social and economic groups of the population is estimated on the basis of the methodology of synthetic data.

scholarly journals Clustering and enhanced classification using a hybrid quantum autoencoder

2021 ◽  
Author(s):  
Maiyuren Srikumar ◽  
Charles Daniel Hill ◽  
Lloyd Hollenberg
Keyword(s):  
Machine Learning ◽  
Supervised Classification ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Data Sets ◽  
New Paradigm ◽  
Novel Approach ◽  
Representational Space ◽  
Quantum Machine Learning ◽  
Pure States

Abstract Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify – and classically represent – their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states – which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

Proposal for dimensionality testing in QPQ

2018 ◽  
Vol 18 (13&14) ◽  
pp. 1125-1142
Author(s):  
Arpita Maitra ◽  
Bibhas Adhikari ◽  
Satyabrata Adhikari
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum System ◽  
Quantum State ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Quantum Private Query ◽  
Unfair Advantage ◽  
Security Proofs

Recently, dimensionality testing of a quantum state has received extensive attention (Ac{\'i}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.

Quantum Error Correction

2020 ◽  
Author(s):  
Todd A. Brun
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Single Photon ◽  
Error Correcting Code ◽  
Quantum Systems ◽  
Quantum Error Correction ◽  
The State ◽  
Quantum States ◽  
Quantum Code ◽  
Quantum Error

Quantum error correction is a set of methods to protect quantum information—that is, quantum states—from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move the state into an error space orthogonal to the original code space while preserving the information in the state. It is possible to determine whether an error has occurred by a suitable measurement and to apply a unitary correction that returns the state to the code space without measuring (and hence disturbing) the protected state itself. In general, codewords of a quantum code are entangled states. No code that stores information can protect against all possible errors; instead, codes are designed to correct a specific error set, which should be chosen to match the most likely types of noise. An error set is represented by a set of operators that can multiply the codeword state. Most work on quantum error correction has focused on systems of quantum bits, or qubits, which are two-level quantum systems. These can be physically realized by the states of a spin-1/2 particle, the polarization of a single photon, two distinguished levels of a trapped atom or ion, the current states of a microscopic superconducting loop, or many other physical systems. The most widely used codes are the stabilizer codes, which are closely related to classical linear codes. The code space is the joint +1 eigenspace of a set of commuting Pauli operators on n qubits, called stabilizer generators; the error syndrome is determined by measuring these operators, which allows errors to be diagnosed and corrected. A stabilizer code is characterized by three parameters [[n,k,d]], where n is the number of physical qubits, k is the number of encoded logical qubits, and d is the minimum distance of the code (the smallest number of simultaneous qubit errors that can transform one valid codeword into another). Every useful code has n>k; this physical redundancy is necessary to detect and correct errors without disturbing the logical state. Quantum error correction is used to protect information in quantum communication (where quantum states pass through noisy channels) and quantum computation (where quantum states are transformed through a sequence of imperfect computational steps in the presence of environmental decoherence to solve a computational problem). In quantum computation, error correction is just one component of fault-tolerant design. Other approaches to error mitigation in quantum systems include decoherence-free subspaces, noiseless subsystems, and dynamical decoupling.

scholarly journals Relationships between body reserve dynamics and rearing performances in meat ewes1

2019 ◽  
Vol 97 (10) ◽  
pp. 4076-4084
Author(s):  
Tiphaine Macé ◽  
Dominique Hazard ◽  
Fabien Carrière ◽  
Sebastien Douls ◽  
Didier Foulquié ◽  
...  
Keyword(s):  
Genetic Relationships ◽  
Genetic Correlations ◽  
Repeated Measurements ◽  
Production Cycle ◽  
Data Sets ◽  
Data Set ◽  
Litter Weight ◽  
Significant Relationships ◽  
Physiological Stage ◽  
Changes Over Time

Abstract The main objective of this work was to study the relationships between body reserve (BR) dynamics and rearing performance (PERF) traits in ewes from a Romane meat sheep flock managed extensively on “Causse” rangelands in the south of France. Flock records were used to generate data sets covering 14 lambing years (YR). The data set included 1,146 ewes with 2 ages of first lambing (AGE), 3 parities (PAR), and 4 litter sizes (LS). Repeated measurements of the BW and BCS were used as indicators of BR. The ewe PERF traits recorded were indirect measurements for maternal abilities and included prolificacy, litter weight and lamb BW at lambing and weaning, ADG at 1, 2, and 3 mo after lambing, and litter survival from lambing to weaning. The effects of different BW and BCS trajectories (e.g., changes in BW and BCS across the production cycle), previously been characterized in the same animals, on PERF traits were investigated. Such trajectories reflected different profiles at the intraflock level in the dynamics of BR mobilization–accretion cycles. Genetic relationships between BR and PERF traits were assessed. All the fixed variables considered (i.e., YR, AGE, PAR, LS, and SEX ratio of the litter) have significant effects on the PERF traits. Similarly, BW trajectories had an effect on the PERF traits across the 3 PARs studied, particularly during the first cycle (PAR 1). The BCS trajectories only affected prolificacy, lamb BW at birth, and litter survival. Most of the PERF traits considered here showed moderate heritabilities (0.17–0.23) except for prolificacy, the lamb growth rate during the third month and litter survival which showed very low heritabilities. With exception of litter survival and prolificacy, ewe PERF traits were genetically, strongly, and positively correlated with BW whatever the physiological stage. A few weak genetic correlations were found between BCS and PERF traits. As illustrated by BW and BCS changes over time, favorable genetic correlations were found, even if few and moderate, between BR accretion or mobilization and PERF traits, particularly for prolificacy and litter weight at birth. In conclusion, our results show significant relationships between BR dynamics and PERF traits in ewes, which could be considered in future sheep selection programs aiming to improve robustness.

scholarly journals Sparsity Based Full Rank Polarimetric Reconstruction of Coherence Matrix T

2019 ◽  
Vol 11 (11) ◽  
pp. 1288 ◽  
Author(s):  
Hossein Aghababaee ◽  
Giampaolo Ferraioli ◽  
Laurent Ferro-Famil ◽  
Gilda Schirinzi ◽  
Yue Huang
Keyword(s):  
Super Resolution ◽  
Full Rank ◽  
Real Data ◽  
Natural Environments ◽  
Data Sets ◽  
Scattering Pattern ◽  
Component Decomposition ◽  
Resolution Imaging ◽  
Processing Techniques ◽  
Physical Features

In the frame of polarimetric synthetic aperture radar (SAR) tomography, full-ranks reconstruction framework has been recognized as a significant technique for fully characterization of superimposed scatterers in a resolution cell. The technique, mainly is characterized by the advantages of polarimetric scattering pattern reconstruction, allows physical feature extraction of the scatterers. In this paper, to overcome the limitations of conventional full-rank tomographic techniques in natural environments, a polarimetric estimator with advantages of super-resolution imaging is proposed. Under the frame of compressive sensing (CS) and sparsity based reconstruction, the profile of second order polarimetric coherence matrix T is recovered. Once the polarimetric coherence matrices of the scatterers are available, the physical features can be extracted using classical polarimetric processing techniques. The objective of this study is to evaluate the performance of the proposed full-rank polarimetric reconstruction by means of conventional three-component decomposition of T, and focusing on the consistency of vertical resolution and polarimetric scattering pattern of the scatterers. The outcomes from simulated and two different real data sets confirm that significant improvement can be achieved in the reconstruction quality with respect to conventional approaches.

The State Wealth-Legislative Compensation Effect

2008 ◽  
Vol 41 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Peverill Squire
Keyword(s):  
United States ◽  
Compensation Effect ◽  
The United States ◽  
The State ◽  
Simple Theory ◽  
The Other ◽  
Data Sets ◽  
Labour Economics ◽  
Economics Literature

Abstract. Legislative scholars have paid almost no attention to explanations for the level of compensation provided to legislators, either within a country or cross-nationally, despite its importance to members and institutions. I posit a simple theory based on state wealth to explain differences in legislative pay. I test this theory using two novel data sets, one on 35 national assemblies, the other on subnational assemblies in Australia, Canada, Germany and the United States. Analysis of these data reveals that national or state wealth is strongly associated with legislator compensation. This finding is consistent with an intriguing analog in the labour economics literature.Résumé. Les érudits du monde législatif ne se sont guère penchés sur les raisons des divers niveaux de rémunération des législateurs, à l'échelle nationale ou transnationale, malgré l'importance du sujet pour les institutions et les membres des législatures. Pour expliquer cette disparité, j'avance une simple théorie fondée sur la richesse des États. J'évalue ensuite cette théorie en m'appuyant sur deux nouvelles bases de données, la première portant sur 35 assemblées nationales et l'autre sur des assemblées sous-nationales en Australie, au Canada, en Allemagne et aux États-Unis. Ces analyses statistiques démontrent qu'il existe effectivement un lien étroit entre la richesse de l'État et la rémunération des législateurs. Cette constatation est confirmée par une analogie fascinante dans la littérature sur l'économique du travail.

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