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In statistical analysis, many classic results require the assumption that models have finite mean or variance, including the most standard versions of the laws of large numbers and the central limit theorems. Such an assumption may not be…
Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic boundary conditions are investigated by means of the $1/N$ expansion and by Monte Carlo simulations. Analytic and numerical results for magnetic susceptibility and…
The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established…
We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency…
A formulation towards quantifying resource count used in a measurement, that is independent of the model of the measurement dynamics(Quantum/Classical), is considered. For any general measurement with $(M+1)$ discrete outcomes, it is found…
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However,…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…
We study the finite-size effects on the deconfinement phase transition (DPT) of hot and / or dense hadronic matter, using a simple thermodynamic model based on the assumption of coexistence of confined and deconfined phases in a finite…
In this letter we study the weak-convergence properties of random variables generated by unsharp quantum measurements. More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit…
Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known as highly relevant, in…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and…
We present an efficient method to extract the amount of true randomness that can be obtained by a Quantum Random Number Generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases,…
We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe…
In this paper we study von Neumann un-biasing normalisation for ideal and real quantum random number generators, operating on finite strings or infinite bit sequences. In the ideal cases one can obtain the desired un-biasing. This relies…
We discuss the implications of finite size effects on the determination of the order of a phase transition which may occur in infinite systems. We introduce a specific model to which we apply different tests. They are aimed to characterise…
Measurement-device-independent quantum key distribution with a finite number of decoy states is analyzed under finite-data-size assumption. By accounting for statistical fluctuations in parameter estimation, we investigate vacuum+weak- and…
In a continuous-variable quantum key distribution (CV-QKD) protocol, which is based on heterodyne detection at the receiver, the application of a noiseless linear amplifier (NLA) on the received signal before the detection can be emulated…
Finite-size error (FSE), the discrepancy between an observable in a finite system and in the thermodynamic limit, is ubiquitous in numerical simulations of quantum many body systems. Although a rough estimate of these errors can be obtained…
Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state,…