Related papers: Quantum j-invariant in positive characteristic I: …
The relations and differences between various classification problems arising in the context of local two-dimensional conformal QFT, modular invariants, and subfactors are discussed. The extent to which locality implies modular invariance,…
The refined Humbert invariant is a positive definite quadratic form intrinsically attached to a curve $C$ of genus 2. This invariant is an algebraic generalization of the (usual) Humbert invariant. This invariant is useful because many…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
We extract genus $0$ consequences of the all genera quantum HRR formula proved in Part IX. This includes re-proving and generalizing the adelic characterization of genus $0$ quantum K-theory found in [Givental A., Tonita V., in Symplectic,…
In this short survey article we collect the current state of the art in the nascent field of \textit{quantum enhancements}, a type of knot invariant defined by collecting values of quantum invariants of knots with colorings by various…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
Quantum characterization, verification, and validation (QCVV) is a set of techniques to probe, describe, and assess the behavior of quantum bits (qubits), quantum information-processing registers, and quantum computers. QCVV protocols probe…
Quantum classification is defined as the task of predicting the associated class of an unknown quantum state drawn from an ensemble of pure states given a finite number of copies of this state. By recasting the state discrimination problem…
A function of positive type can be defined as a positive functional on a convolution algebra of a locally compact group. In the case where the group is abelian, by Bochner's theorem a function of positive type is, up to normalization, the…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…
The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this…
We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Quantum nonlocal correlation (QNC) is thought to be more general than quantum entanglement correlation, but the strength of it has not been well defined. We propose a way to measure the strength of QNC basing on the characteristic function.…
We continue our study of the genus-$0$ permutation-equivariant quantum K-theory of the target $X=pt$, and completely determine the "big J-function" of this theory. The computation is based on the application of Lefschetz' fixed point…
The aim of these two papers (I and II) is to try to give fundamental concepts of quantum kinematics to q-deformed quantum spaces. Paper I introduces the relevant mathematical concepts. A short review of the basic ideas of q-deformed…
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed…