Related papers: On the Information of the Second Moments Between R…
In this paper, we consider the problem of Mutually Unbiased Bases in prime dimension $d$. It is known to provide exactly $d+1$ mutually unbiased bases. We revisit this problem using a class of circulant $d \times d$ matrices. The…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
This study investigates non-adiabatic wave dynamics in condensed media and the transition from adiabatic stability to spectral chaos. We introduce a dimensionless parameter, as a universal metric to quantify phase-mode redistribution at…
We describe a Bayesian framework for estimating the time-domain noise covariance of CMB observations, typically parametrized in terms of a 1/f frequency profile. This framework is based on the Gibbs sampling algorithm, which allows for…
Standard variational lower bounds used to train latent variable models produce biased estimates of most quantities of interest. We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models…
Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes…
The integrated information theory is thought to be a key clue towards the theoretical understanding of consciousness. In this study, we propose a simple numerical model comprising a set of coupled double quantum dots, where the…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion.…
Measurements can be viewed as interactions between a measured system and a pointer system that imprint information about the system on the pointer. For so-called unbiased interactions, the measurement statistics--the information…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
In this paper we review the application of the matched filter (MF) technique and its application to detect weak, deterministic, smooth signals in a stationary, random, Gaussian noise. This is particular suitable in astronomy to detect…
Sparse wearable inertial measurement units (IMUs) have gained popularity for estimating 3D human motion. However, challenges such as pose ambiguity, data drift, and limited adaptability to diverse bodies persist. To address these issues, we…
Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the…
Continual learning in environments with shifting data distributions is a challenging problem with several real-world applications. In this paper we consider settings in which the data distribution(task) shifts abruptly and the timing of…
Efficient understanding of a quantum system fundamentally relies on the selection of observables. Pauli observables and mutually unbiased bases (MUBs) are widely used in practice and are often regarded as theoretically optimal for quantum…
We study some of the most commonly used mutual information estimators, based on histograms of fixed or adaptive bin size, $k$-nearest neighbors and kernels, and focus on optimal selection of their free parameters. We examine the consistency…
Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with…
We introduce a novel strategy, based on the use of modular variables, to encode and deterministically process quantum information using states described by continuous variables. Our formalism leads to a general recipe to adapt existing…
A unified approach to (symmetric informationally complete) positive operator valued measures and mutually unbiased bases is developed in this article. The approach is based on the use of operator equivalents expanded in the enveloping…