Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

COSMOS

QUANTUM INFORMATION, ENTANGLEMENT AND RELATIONSHIPS

Thomas Durt

Published May 1, 2006• 4 citations
Publisher

Abstract

We present several physical applications that were generated in the framework of quantum information science. We emphasize the crucial role played, in this approach, by a group of unitary transformations, the generalized Pauli or Heisenberg–Weyl group, and by a non-classical property, called entanglement, which appears to be a basic ingredient in Quantum Information Theory. We sketch the links between entanglement and non-locality, and discuss an analogy between entanglement and (human) relationships.

DOI
10.1142/s0219607706000146

Related papers

Classical Entanglement: Theory and Application

Falk Töppel, Andrea Aiello, Christoph Marquardt +2 more

Quantum information theory shows that quantum measurements have the essential capability to provide more information than classical ones, as emphasized by many authors [1, 2]. Exploiting the advantages of entanglement makes this possible. Several works based on the concept of quantum measurements have appeared recently [3–5]. However, for the purpose of such measurements, not all the features of quantum entanglement are necessary. For example most quantum measurements require entanglement as primary resource, but not non-locality, which is a different property [6].

European Quantum Electronics Conference (EQEC)•Jun 21, 2015•4 citations

Outlook

Vlatko Vedral

Abstract This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.

•Sep 28, 2006•0 citations

Two Realities: Quantum Entanglment versus Non-Locality

Michele Caponigro

We argue, from epistemological point of view, the relationship between quantum entanglement and non-locality in quantum mechanics. The questions of how to quantify entanglement and non-locality and the need to clarify the relationship between them are important not only conceptually, but also practically, insofar as entanglement and non-locality seem to be different resources for the performance of quantum information processing tasks. Quantum information science is in the process of transforming our understanding of both QM and information theory.

Prespacetime journal•Nov 23, 2017•0 citations

The Subtleties of Entanglement and its Role in Quantum Information Theory

Rob Clifton

My aim in this paper is a modest one. I do not have any particular thesis to advance about the nature of entanglement, nor can I claim novelty for any of the material I shall discuss. My aim is simply to raise some questions about entanglement that spring naturally from certain developments in quantum information theory and are, I believe, worthy of serious consideration by philosophers of science. The main topics I discuss are different manifestations of quantum nonlocality, entanglement-assisted communication, and entanglement thermodynamics.

Philosophy of Science•Sep 1, 2002•10 citations

Efficient Quantum Fourier Transforms For Semisimple Algebras

Ben Foxman, Barak Nehoran, Yongshan Ding

The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we extend the framework for the QFT from finite groups to finite-dimensional semisimple algebras, and give efficient QFTs for the partition algebra $P_n(d)$, Brauer algebra $B_n(d)$, and walled Brauer algebra $B_{r,s}(d)$. These algebras play important roles in generalized Schur-Weyl duality, statistical physics and many-body systems, and have recently found several applications in quantum algorithms. Unlike the group case, the Fourier transform over a semisimple algebra can be non-unitary. Nevertheless, we show that when the parameter $d$ is sufficiently large, the Fourier transform is well approximated by a unitary operator. Furthermore, we show that for each of the algebras $A$ from above, such an approximate Fourier transform can be implemented efficiently: we give a quantum algorithm with gate complexity $\mathrm{poly}(n,\log d,\log(1/\varepsilon))$ for approximating the Fourier transform to error $(d^{-1/2} + \varepsilon) \cdot \mathrm{poly}(|A|)$. Along the way, we establish several properties of the Fourier basis of semisimple algebras that may be of independent interest.

quant-pharXiv:2605.05337•May 8, 2026•0 citations

LINKS AND QUANTUM ENTANGLEMENT

A. I. Solomon, CHOON-LIN HO

We discuss the analogy between topological entanglement and quantum entanglement, particularly for tripartite quantum systems. We illustrate our approach by first discussing two clearly (topologically) inequivalent systems of three-ring links: The Borromean rings, in which the removal of any one link leaves the remaining two non-linked (or, by analogy, non-entangled); and an inequivalent system (which we call the NUS link) for which the removal of any one link leaves the remaining two linked (or, entangled in our analogy). We introduce unitary representations for the appropriate Braid Group ($B_3$) which produce the related quantum entangled systems. We finally remark that these two quantum systems, which clearly possess inequivalent entanglement properties, are locally unitarily equivalent.

arXiv:1104.5144•Conference in Honour of Murray Gell-Mann's 80th Birthday•Nov 1, 2010•2 citations
We present several physical applications that were generated in the framework of quantum information science. We emphasize the crucial role played, in this approach, by a group of unitary transformations, the generalized Pauli or Heisenberg–Weyl group, and by a non-classical property, called entanglement, which appears to be a basic ingredient in Quantum Information Theory. We sketch the links between entanglement and non-locality, and discuss an analogy between entanglement and (human) relationships.
Quantum information theory shows that quantum measurements have the essential capability to provide more information than classical ones, as emphasized by many authors [1, 2]. Exploiting the advantages of entanglement makes this possible. Several works based on the concept of quantum measurements have appeared recently [3–5]. However, for the purpose of such measurements, not all the features of quantum entanglement are necessary. For example most quantum measurements require entanglement as primary resource, but not non-locality, which is a different property [6].
Abstract This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.
We argue, from epistemological point of view, the relationship between quantum entanglement and non-locality in quantum mechanics. The questions of how to quantify entanglement and non-locality and the need to clarify the relationship between them are important not only conceptually, but also practically, insofar as entanglement and non-locality seem to be different resources for the performance of quantum information processing tasks. Quantum information science is in the process of transforming our understanding of both QM and information theory.
My aim in this paper is a modest one. I do not have any particular thesis to advance about the nature of entanglement, nor can I claim novelty for any of the material I shall discuss. My aim is simply to raise some questions about entanglement that spring naturally from certain developments in quantum information theory and are, I believe, worthy of serious consideration by philosophers of science. The main topics I discuss are different manifestations of quantum nonlocality, entanglement-assisted communication, and entanglement thermodynamics.
The quantum Fourier transform (QFT) is a fundamental primitive in quantum computation and quantum information. In this work, we extend the framework for the QFT from finite groups to finite-dimensional semisimple algebras, and give efficient QFTs for the partition algebra Pn(d)P_n(d)Pn​(d), Brauer algebra Bn(d)B_n(d)Bn​(d), and walled Brauer algebra Br,s(d)B_{r,s}(d)Br,s​(d). These algebras play important roles in generalized Schur-Weyl duality, statistical physics and many-body systems, and have recently found several applications in quantum algorithms. Unlike the group case, the Fourier transform over a semisimple algebra can be non-unitary. Nevertheless, we show that when the parameter ddd is sufficiently large, the Fourier transform is well approximated by a unitary operator. Furthermore, we show that for each of the algebras AAA from above, such an approximate Fourier transform can be implemented efficiently: we give a quantum algorithm with gate complexity poly(n,log⁡d,log⁡(1/ε))\mathrm{poly}(n,\log d,\log(1/\varepsilon))poly(n,logd,log(1/ε)) for approximating the Fourier transform to error (d−1/2+ε)⋅poly(∣A∣)(d^{-1/2} + \varepsilon) \cdot \mathrm{poly}(|A|)(d−1/2+ε)⋅poly(∣A∣). Along the way, we establish several properties of the Fourier basis of semisimple algebras that may be of independent interest.
We discuss the analogy between topological entanglement and quantum entanglement, particularly for tripartite quantum systems. We illustrate our approach by first discussing two clearly (topologically) inequivalent systems of three-ring links: The Borromean rings, in which the removal of any one link leaves the remaining two non-linked (or, by analogy, non-entangled); and an inequivalent system (which we call the NUS link) for which the removal of any one link leaves the remaining two linked (or, entangled in our analogy). We introduce unitary representations for the appropriate Braid Group (B3B_3B3​) which produce the related quantum entangled systems. We finally remark that these two quantum systems, which clearly possess inequivalent entanglement properties, are locally unitarily equivalent.