Related papers: A Meaner King uses Biased Bases

We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…

The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…

This paper shows that the common method used for making predictions under uncertainty in A1 and science is in error. This method is to use currently available data to select the best model from a given class of models-this process is called…

The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We…

The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the…

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…

We introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new classical limit formulation. This formulation…

We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…

We revisit the problem of mutually unbiased measurements in the context of estimating the unknown state of a $d$-level quantum system, first studied by W. K. Wootters and B. D. fields[7] in 1989 and later investigated by S. Bandyopadhyay et…

A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…

The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset…

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance…

Quantum Monte Carlo is one of the most promising approaches for dealing with large-scale quantum many-body systems. It has played an extremely important role in understanding strongly correlated physics. However, two fundamental problems,…

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models…

State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…

We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…

We address the problem of reconstructing quantum theory from the perspective of an agent who makes bets about the outcomes of possible experiments. We build a general Bayesian framework that can be used to organize the agent's beliefs and…

We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…

Classical Bayes' rule lays the foundation for the classical causal relation between cause (input) and effect (output). This causal relation is believed to be universally true for all physical processes. Here we show, on the contrary, that…

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…