相关论文: The quantization of the standard triadic Cantor di…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…
In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
For uniform scalar quantization, the error distribution is approximately a uniform distribution over an interval (which is also a 1-dimensional ball). Nevertheless, for lattice vector quantization, the error distribution is uniform not over…
Let $\mu$ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of $\mathbb R^k$. We study the Hausdorff and the packing dimensions, and the quantization dimensions…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized processing. This includes (potentially non-computable) measures…
The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time -series of events observed for a trapped ion, electron or any other individual physical system. The…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…
The Kochen-Specker theorem states that exclusive and complete deterministic outcome assignments are impossible for certain sets of measurements, called Kochen-Specker (KS) sets. A straightforward consequence is that KS sets do not have…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach…
QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit…
Quantification, i.e., the task of training predictors of the class prevalence values in sets of unlabeled data items, has received increased attention in recent years. However, most quantification research has concentrated on developing…
Stochastic quantisation normally involves the introduction of a fictitious extra time parameter, which is taken to infinity so that the system evolves to an equilibrium state.In the case of a locally supersymmetric theory, an interesting…
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
Quantile is an important risk measure quantifying the stochastic system random behaviors. This paper studies a pooled quantile estimator, which is the sample quantile of detailed simulation outputs after directly pooling independent sample…
The main aim of the paper is to introduce a new class of (semigroup-valued) measures that are ultrahomogeneous on the Boolean algebra of all clopen subsets of the Cantor space and to study their automorphism groups. A characterisation, in…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…