scholarly journals Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras

2017 ◽  
Vol 236 ◽  
pp. 161-173 ◽  
Author(s):  
Mathys Rennela ◽  
Sam Staton ◽  
Robert Furber
Keyword(s):  
Quantum Foundations ◽  
Matrix Algebras ◽  
Infinite Dimensionality

Notes on three-pass protocol

2020 ◽  
Vol 25 (4) ◽  
pp. 4-9
Author(s):  
Yerzhan R. Baissalov ◽  
Ulan Dauyl
Keyword(s):  
Finite Fields ◽  
Matrix Algebras ◽  
Associative Structures

The article discusses primitive, linear three-pass protocols, as well as three-pass protocols on associative structures. The linear three-pass protocols over finite fields and the three-pass protocols based on matrix algebras are shown to be cryptographically weak.

News on Quantum Foundations of Consciousness

1990 ◽  
Vol 70 (3) ◽  
pp. 930-930 ◽  
Author(s):  
Alexander A. Berezin
Keyword(s):  
Quantum Foundations

scholarly journals Quantum postulate vs. quantum nonlocality: on the role of the Planck constant in Bell’s argument

2021 ◽  
Vol 51 (1) ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Nonlocality ◽  
Quantum Mechanical ◽  
Quantum Foundations ◽  
Planck Constant ◽  
Variable Model ◽  
Basic Principles ◽  
Fundamental Feature ◽  
Hidden Variable ◽  
Bell Model

AbstractWe present a quantum mechanical (QM) analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of QM, Bell’s model implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck.

scholarly journals Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zheng-Hao Liu ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Mu Yang ◽  
Qiang Li ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Success Probability ◽  
Quantum Foundations ◽  
Mixed States ◽  
Graph States ◽  
Hardy Type ◽  
Realistic Description ◽  
Entanglement Detection ◽  
Quantum Paradoxes

AbstractThe Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

scholarly journals Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Clifford Algebras ◽  
Discrete Systems ◽  
Complex Numbers ◽  
Majorana Fermions ◽  
Matrix Algebras ◽  
Dirac Equations ◽  
Points Of View

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

scholarly journals Lattice-Ordered Matrix Algebras Over Real GCD-Domains

2013 ◽  
Vol 41 (6) ◽  
pp. 2109-2113
Author(s):  
Fei Li ◽  
Xianlong Bai ◽  
Derong Qiu
Keyword(s):  
Matrix Algebras

The length function and matrix algebras

2013 ◽  
Vol 193 (5) ◽  
pp. 687-768 ◽  
Author(s):  
O. V. Markova
Keyword(s):  
Length Function ◽  
Matrix Algebras
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