Related papers: Fermionic quantum operations: a computational fram…
Quantum computational models can be approached via the lens of resources needed to perform computational tasks, where a computational advantage is achieved by consuming specific forms of quantum resources, or, conversely, resource-free…
In this paper, a functional model of interactions in quantum theory (QT) is proposed. A functional model describes the dynamic evolution of a physical system in terms of process steps and intermediate states. That is, it describes how…
We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.
We introduce Kadanoff-Ceva order-disorder operators in the quantum Ising model. This approach was first used for the classical planar Ising model and recently put back to the stage. This representation turns out to be equivalent to the loop…
We propose a theory of characterizing quantum circuits with qubit functional configurations. Any quantum circuit can be decomposed into alternating sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares the current…
The fermionic sector of the Standard Model of Elementary Particles emerges as the low energy limit of a single fermionic field freely propagating in a higher dimensional background. The local geometrical framework is obtained by enforcing…
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…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
In this paper, we have introduced the Prabhakar fractional $q$-integral and $q$-differential operators. We first study the semi-group property of the Prabhakar fractional $q$-integral operator, which allowed us to introduce the…
Any quantum resource theory is based on free states and free operations, i.e., states and operations which can be created and performed at no cost. In the resource theory of coherence free states are diagonal in some fixed basis, and free…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
The quantum integer [n]_q is the polynomial 1 + q + q^2 + ... + q^{n-1}, and the sequence of polynomials { [n]_q }_{n=1}^{\infty} is a solution of the functional equation f_{mn}(q) = f_m(q)f_n(q^m). In this paper, semidirect products of…
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
Considerable work has recently been directed toward developing resource theories of quantum coherence. In most approaches, a state is said to possess quantum coherence if it is not diagonal in some specified basis. In this letter we…
This article gives a brief introduction to $q$-special functions, i.e., $q$-analogues of the classical special functions. Here $q$ is a deformation parameter, usually $0<q<1$, where $q=1$ is the classical case. The main topics to be treated…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Quantum phase transitions have been the subject of intense investigations in the last two decades [1]. Among other problems, these phase transitions are relevant in the study of heavy fermion systems, high temperature superconductors and…
The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in…
We extend our sum over topologies formula to fermions. We show that fermionic fields display an instability with respect to topology fluctuations. We present some phenomenological arguments for a modification of the action in the case of…