Related papers: Notes on the weak positivity theorems

The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.

The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…

The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be…

This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…

We propose two distinct interpretations of extended probabilities which are realistic for the physical world.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative…

In the article 'Criteria for Strong and Weak Random Attractors' necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.

In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such…

We investigate weak approximation away from a finite set of places for a class of biquadratic fourfolds inside $\mathbb{P}^3 \times \mathbb{P}^2$, some of which appear in the recent work of Hassett--Pirutka--Tschinkel.

We discuss the preceding Comment and conclude that the arguments given there against the relevance of null weak values as representing the absence of a system property are not compelling. We give an example in which the transition matrix…

The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then,…

Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be…

In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…

We obtain simple proofs of certain inequalites for bivariate means.

Weak value amplification (WVA) is a concept that has been extensively used in a myriad of applications with the aim of rendering measurable tiny changes of a variable of interest. In spite of this, there is still an on-going debate about…

A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…

A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…