scholarly journals On the Prospects of Multiport Devices for Photon-Number-Resolving Detection

2019 ◽  
Vol 1 (2) ◽  
pp. 162-180 ◽  
Author(s):  
Yong Siah Teo ◽  
Hyunseok Jeong ◽  
Jaroslav Řeháček ◽  
Zdeněk Hradil ◽  
Luis L. Sánchez-Soto ◽  
...  
Keyword(s):  
Transfer Function ◽  
Mean Squared Error ◽  
Photon Number ◽  
Finite Size ◽  
Analytical Framework ◽  
Resolving Power ◽  
State Measurement ◽  
Fock State ◽  
Probability Simplex ◽  
Asymptotic Mean Squared Error

Ideal photon-number-resolving detectors form a class of important optical components in quantum optics and quantum information theory. In this article, we theoretically investigate the potential of multiport devices having reconstruction performances approaching that of the Fock-state measurement. By recognizing that all multiport devices are minimally complete, we first provide a general analytical framework to describe the tomographic accuracy (or quality) of these devices. Next, we show that a perfect multiport device with an infinite number of output ports functions as either the Fock-state measurement when photon losses are absent or binomial mixtures of Fock-state measurements when photon losses are present and derive their respective expressions for the tomographic transfer function. This function is the scaled asymptotic mean squared error of the reconstructed photon-number distributions uniformly averaged over all distributions in the probability simplex. We then supply more general analytical formulas for the transfer function for finite numbers of output ports in both the absence and presence of photon losses. The effects of photon losses on the photon-number resolving power of both infinite- and finite-size multiport devices are also investigated.

scholarly journals Threshold selection in univariate extreme value analysis

Extremes ◽  
2021 ◽  
Author(s):  
Laura Fee Schneider ◽  
Andrea Krajina ◽  
Tatyana Krivobokova
Keyword(s):  
Mean Squared Error ◽  
Extreme Value ◽  
Hill Estimator ◽  
Small Samples ◽  
Extreme Value Analysis ◽  
Threshold Selection ◽  
Value Analysis ◽  
Wide Range ◽  
Asymptotic Mean Squared Error ◽  
The Hill

AbstractThreshold selection plays a key role in various aspects of statistical inference of rare events. In this work, two new threshold selection methods are introduced. The first approach measures the fit of the exponential approximation above a threshold and achieves good performance in small samples. The second method smoothly estimates the asymptotic mean squared error of the Hill estimator and performs consistently well over a wide range of processes. Both methods are analyzed theoretically, compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time.

scholarly journals An Optimal Tail Selection in Risk Measurement

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 70
Author(s):  
Małgorzata Just ◽  
Krzysztof Echaust
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Random Variable ◽  
Threshold Level ◽  
Middle Part ◽  
Risk Measurement ◽  
Practical Applications ◽  
Tuning Parameters ◽  
Path Stability ◽  
Asymptotic Mean Squared Error

The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in risk measurement. The results indicate which method may be useful in practice for investors and financial and regulatory institutions. Some methods that perform well in simulation studies, based on theoretical distributions, may not perform well when real data are in use. We analyze twelve methods with different parameters for forty-eight world indices using returns from the period of 2000–Q1 2020 and four sub-periods. The research objective is to compare the methods and to identify those which can be recognized as useful in risk measurement. The results suggest that only four tail selection methods, i.e., the Path Stability algorithm, the minimization of the Asymptotic Mean Squared Error approach, the automated Eyeball method with carefully selected tuning parameters and the Hall single bootstrap procedure may be useful in practical applications.

Resolving Power and the Detection of Linear Detail

1965 ◽  
Vol 19 (2) ◽  
pp. 190-205 ◽  
Author(s):  
W. N. Charman
Keyword(s):  
Transfer Function ◽  
Spatial Frequency ◽  
Resolving Power ◽  
Optical Transfer Function ◽  
Simple Relationship ◽  
Frequency Spectra ◽  
Optical Transfer

The ability of a photographic system to resolve and detect linear details is discussed in terms of the spatial frequency spectra of the details, the optical transfer function of the system and the threshold of the detector used with the system. It is shown that there is no simple relationship between the resolving power of the system and the size of the linear detail that the system is capable of detecting.

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

INFLUENCE OF THE COUNTER-ROTATING TERMS ON THE RABI OSCILLATIONS IN THE POLYATOMIC JAYNES-CUMMINGS MODEL WITH CAVITY LOSSES FOR INITIAL FOCK-STATE FIELDS

1996 ◽  
Vol 10 (26) ◽  
pp. 1311-1322
Author(s):  
J. SEKE
Keyword(s):  
Dipole Moment ◽  
Time Evolution ◽  
Population Inversion ◽  
Photon Number ◽  
Numerical Results ◽  
Rabi Oscillations ◽  
Virtual Photons ◽  
Fock State ◽  
The Mean ◽  
Atomic Population Inversion

The significance of the counter-rotating terms in the polyatomic Jaynes-Cummings model with cavity losses is demonstrated. Numerical results for the time evolution of the atomic population inversion and dipole moment for an initial Fock-state field with different photon numbers are presented for various cavity dampings. The appearance of new steady states for the population inversion and the mean-photon number under the influence of the counter-rotating terms is pointed out. Namely, as is shown, the presence of “virtual photons”, produced by the counter-rotating terms, leads to these effects.

scholarly journals Box-Jenkins Transfer Function Modelling for Reliable Determination of VO2 Kinetics in Patients with COPD

2019 ◽  
Vol 9 (9) ◽  
pp. 1822 ◽  
Author(s):  
Joren Buekers ◽  
Jan Theunis ◽  
Alberto Peña Fernández ◽  
Emiel F. M. Wouters ◽  
Martijn A. Spruit ◽  
...  
Keyword(s):  
Transfer Function ◽  
Mean Squared Error ◽  
Kinetic Feature ◽  
Reliable Determination ◽  
Exponential Models ◽  
Mean Response Time ◽  
Vo2 Kinetics ◽  
Constant Work Rate ◽  
Function Modelling ◽  
Feature Values

Oxygen uptake (VO2) kinetics provide information about the ability to respond to the increased physical load during a constant work rate test (CWRT). Box-Jenkins transfer function (BJ-TF) models can extract kinetic features from the phase II VO2 response during a CWRT, without being affected by unwanted noise contributions (e.g., phase I contribution or measurement noise). CWRT data of 18 COPD patients were used to compare model fits and kinetic feature values between BJ-TF models and three typically applied exponential modelling methods. Autocorrelation tests and normalised root-mean-squared error values (BJ-TF: 2.8 ± 1.3%; exponential methods A, B and C: 10.5 ± 5.8%, 11.3 ± 5.2% and 12.1 ± 7.0%; p < 0.05) showed that BJ-TF models, in contrast to exponential models, could account for the most important noise contributions. This led to more reliable kinetic feature values compared to methods A and B (e.g., mean response time (MRT), BJ-TF: 74 ± 20 s; methods A-B: 100 ± 56 s–88 ± 52 s; p < 0.05). Only exponential modelling method C provided kinetic feature values comparable to BJ-TF features values (e.g., MRT: 75 ± 20 s). Based on theoretical considerations, we recommend using BJ-TF models, rather than exponential models, for reliable determinations of VO2 kinetics.

scholarly journals Estimating a Finite Population Mean Using Transformed Data in Presence of Random Nonresponse

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Nelson Kiprono Bii ◽  
Christopher Ouma Onyango ◽  
John Odhiambo
Keyword(s):  
Finite Population ◽  
Mean Squared Error ◽  
Simulated Data ◽  
Sampling Technique ◽  
Theory And Practice ◽  
Sample Survey ◽  
Population Mean ◽  
Data Weighting ◽  
Asymptotic Mean Squared Error ◽  
Mean Variance

Developing finite population estimators of parameters such as mean, variance, and asymptotic mean squared error has been one of the core objectives of sample survey theory and practice. Sample survey practitioners need to assess the properties of these estimators so that better ones can be adopted. In survey sampling, the occurrence of nonresponse affects inference and optimality of the estimators of finite population parameters. It introduces bias and may cause samples to deviate from the distributions obtained by the original sampling technique. To compensate for random nonresponse, imputation methods have been proposed by various researchers. However, the asymptotic bias and variance of the finite population mean estimators are still high under this technique. In this paper, transformation of data weighting technique is suggested. The proposed estimator is observed to be asymptotically consistent under mild assumptions. Simulated data show that the estimator proposed is much better than its rival estimators for all the different mean functions simulated.

Experimental resources needed to implement photon number splitting attack in quantum cryptography

2022 ◽  
Vol 19 (2) ◽  
pp. 025203
Author(s):  
S P Kulik ◽  
K S Kravtsov ◽  
S N Molotkov
Keyword(s):  
Coherent State ◽  
Quantum Key Distribution ◽  
Distribution Systems ◽  
Communication Channel ◽  
Random Phase ◽  
Photon Number ◽  
Fock States ◽  
Fock State ◽  
Experimental Parameters ◽  
Photon Number Splitting Attack

Abstract The analysis of the security of quantum key distribution systems with respect to an attack with nondemolishing measurement of the number of photons (photon number splitting—PNS attack) is carried out under the assumption that in the communication channel in each parcel there is a pure Fock state with a different number of photons, and the distribution of states by number of photons has Poisson statistics. In reality, in the communication channel in each parcel there are not individual Fock states, but a pure coherent state with a random phase—a superposition of Fock states with different numbers of photons. The paper analyzes the necessary experimental resources necessary to prepare individual Fock states with a certain number of photons from the superposition of Fock states for a PNS attack. Optical schemes for implementing such an attack are given, and estimates of experimental parameters at which a PNS attack is possible are made.

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