相关论文: Strict Bounds on Franson Inequality

We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation; and the analysis of…

Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…

We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…

The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new…

We improve constants in the Rademacher-Menchov inequality.

This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The…

The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…

Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…

Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…

We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty…

In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…

Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…

A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…

This article discusses the main aspects related to Bell's inequality, both theoretical and experimental. A new derivation of Bell's inequality is also presented, which stands out for its mathematical simplicity. The exposition is mainly…

In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement…

Lindsay and Basak (2000) posed the question of how far from normality could a distribution be if it matches $k$ normal moments. They provided a bound on the maximal difference in c.d.f.'s, and implied that these bounds were attained. It…

A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant and phenomenological model of dissipation) is known to be in odds with the detailed balance in the thermodynamic limit. We show that this is…

There has been recently a lot of research on sparse variants of random projections, faster adaptations of the state-of-the-art dimensionality reduction technique originally due to Johsnon and Lindenstrauss. Although the construction is very…