Related papers: Quantization for a condensation system
We introduce the notion of compatibility dimension for a set of quantum measurements: it is the largest dimension of a Hilbert space on which the given measurements are compatible. In the Schr\"odinger picture, this notion corresponds to…
This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of random measurements. The main contributions include the…
We consider a sequence of idealized measurements of time-separation $\Delta t$ onto a discrete one-dimensional disordered system. A connection with Markov chains is found. For a rapid sequence of measurements, a diffusive regime occurs and…
Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly…
This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that…
In the critical task of making generative models trustworthy and robust, methods for Uncertainty Quantification (UQ) have begun to show encouraging potential. However, many of these methods rely on rigid heuristics that fail to generalize…
It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the…
We consider the phenomenon of condensation of a globally conserved quantity $H=\sum_{i=1}^N \epsilon_i$ distributed on $N$ sites, occurring when the density $h= H/N$ exceeds a critical density $h_c$. We numerically study the dependence of…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
We address the problem of network quantization, that is, reducing bit-widths of weights and/or activations to lighten network architectures. Quantization methods use a rounding function to map full-precision values to the nearest quantized…
Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical…
In Dataset Condensation, the goal is to synthesize a small dataset that replicates the training utility of a large original dataset. Existing condensation methods synthesize datasets with significant redundancy, so there is a dire need to…
We study the perturbation of a measure $\mu \in \mathscr{P}(\mathbb{R})$ consisting in superposing two copies of $\mu$, each slightly shifted by a small distance $\pm h$. The difference between $\mu$ and its perturbation is measured with a…
Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…
We study the set $M_\infty(X)$ of all infinite full non-atomic Borel measures on a Cantor space X. For a measure $\mu$ from $M_\infty(X)$ we define a defective set $M_\mu = \{x \in X : for any clopen set U which contains x we have \mu(U) =…
This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…
We propose a measure of non-classical correlations in bipartite quantum states based on local unitary operations. We prove the measure is non-zero if and only if the quantum discord is non-zero; this is achieved via a new characterization…
The density of bosonic states are calculated for spinless free massive bosons in generalised d dimensions. The number of bosons are calculated in the lowest energy state. The Bose Einstein condensation was found in generalised dimensions…
Properties of the law $\mu$ of the integral $\int_0^{\infty}c^{-N_{t-}}\,dY_t$ are studied, where $c>1$ and $\{(N_t,Y_t),t\geq0\}$ is a bivariate L\'{e}vy process such that $\{N_t\}$ and $\{Y_t\}$ are Poisson processes with parameters $a$…
For d nonpolar compact sets K_1,...,K_d in the complex plane, d admissible weights Q_1,...,Q_d, and a positive semidefinite d x d interaction matrix C with no zero column, we define natural discretizations of the associated weighted vector…