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

Entanglement—A Higher Order Symmetry

Paul O’Hara

Published Feb 15, 2023• 1 citation
Publisher

Abstract

Can we accurately model the spin state of a quantum particle? If so, we should be able to make identical copies of such a state and also obtain its mirror image. In quantum mechanics, many subatomic particles can form entangled pairs that are mirror images of each other, although the state of an individual particle cannot be duplicated or cloned as experimentally demonstrated by Aspect, Clauser and Zeilinger, the winners of the Nobel Prize in Physics 2022. We show that there is a higher-order symmetry associated with the SL(2,C) group that underlies the singlet state, which means that the singlet pairing preserves Lorentz transformations independently of the metric used. The Pauli exclusion principle can be derived from this symmetry.

DOI
10.3390/ecu2023-14011

Related papers

Particle Interactions and Quantum Entanglement in High-Energy Collisions

Emidio Gabrielli A

The exploration of fundamental quantum phenomena, such as entanglement and Bell inequality violations—extensively studied in low-energy regimes—has recently extended to high-energy particle collisions. Experimentally, Bell inequality violations, which challenge Einstein’s principle of local realism, were first observed in low-energy entangled photon systems by A. Aspect, J. F. Clauser, and A. Zeilinger, earning them the 2022 Nobel Prize in Physics. Particle colliders provide a novel setting for probing quantum information theory, operating at energies over 10 orders of magnitude higher than previous experiments and in the presence of electroweak and strong interactions. Additionally, collider detectors offer unique advantages for quantum state reconstruction via quantum state tomography. This book chapter reviews key theoretical and experimental advancements in this emerging field, highlighting its challenges, objectives, and potential impact on both quantum information theory and high-energy physics.

arXiv:2509.07585•IntechOpen eBooks•Nov 21, 2025•1 citation

An Open Letter to the 2022 Winners of the Nobel Prize in Physics

Andre Vatarescu

The theoretical concept of photonic quantum nonlocality cannot be implemented physically because of the quantum Rayleigh scattering of single photons. A distinction needs to be made between the correlation of individual, single measurements of pure states and the correlation of the measured ensembles of mixed states. The correlation operator of Pauli vector operators delivers the same probabilities of correlated detections of photons for both independent and multi-photon states as for ‘entangled’ states of photons. As single-photon sources are not needed, the design and implementation of quantum computing operations and other devices will be significantly streamlined.

IgMin Research•Oct 28, 2024•0 citations

Relativistic Effects in Quantum Entanglement

Nicolai Friis

One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by violating Bell inequalities. While the role of entanglement is well studied in the realm of nonrelativistic quantum mechanics, its significance in a relativistic quantum theory is a relatively new field of interest. In this work the consequences of a relativistic description of quantum entanglement are discussed. We analyze the representations of the symmetry groups of special relativity, i.e. of the Lorentz group, and the Poincaré group, on the Hilbert space of states. We describe how unitary, irreducible representations of the Poincaré group for massive spin 1/2 particles are constructed from representations of Wigner's little group. We then proceed to investigate the role of the Wigner rotations in the transformation of quantum states under a change of inertial reference frame. Considering different partitions of the Hilbert space of 2 particles, we find that the entanglement of the quantum states appears different in different inertial frames, depending on the form of the states, the chosen inertial frames, and the particular choice of partition. It is explained, how, despite of this, the maximally possible violation of Bell inequalities is frame independent, when using appropriate spin observables, which are related to the Pauli-Ljubanski vector, a Casimir operator of the Poincaré group.

arXiv:1003.1874•Jan 1, 2010•35 citations

The Laureates of the Nobel Prize in Physics 2022. Some personal memories

Reinhold A. Bertlmann

Some personal memories of the Nobel Prize Winners 2022 Alain Aspect, John Clauser, and Anton Zeilinger are summarized and the significance of their works is described in a historical perspective.

arXiv:2302.03736•Feb 7, 2023•0 citations

Higher-order quantum entanglement

Anton Zeilinger, Michael Horne, Daniel M. Greenberger

In quantum mechanics, the general state describing two or more particles is a linear superposition of product states. Such a superposition is called entangled if it cannot be factored into just one product. When only two particles are entangled, the stage is set for Einstein-Podolsky-Rosen (EPR) discussions and Bell's proof that the EPR viewpoint contradicts quantum mechanics. If more than two particles are involved, new possibilities and phenomena arise. For example, the Greenberger, Horne, and Zeilinger (GHZ) disproof of EPR applies. Furthermore, as we point out, with three or more particles even entanglement itself can be an entangled property.

•Feb 1, 1992•30 citations

Single-particle entanglement

M Ali Can, Alexander A. Klyachko, A.S. Shumovsky

Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single ‘spin-1’ particle. We give physical examples related to photons and condensed matter physics.

arXiv:quant-ph/0409208•Journal of Optics B Quantum and Semiclassical Optics•Jan 7, 2005•33 citations
Can we accurately model the spin state of a quantum particle? If so, we should be able to make identical copies of such a state and also obtain its mirror image. In quantum mechanics, many subatomic particles can form entangled pairs that are mirror images of each other, although the state of an individual particle cannot be duplicated or cloned as experimentally demonstrated by Aspect, Clauser and Zeilinger, the winners of the Nobel Prize in Physics 2022. We show that there is a higher-order symmetry associated with the SL(2,C) group that underlies the singlet state, which means that the singlet pairing preserves Lorentz transformations independently of the metric used. The Pauli exclusion principle can be derived from this symmetry.
The exploration of fundamental quantum phenomena, such as entanglement and Bell inequality violations—extensively studied in low-energy regimes—has recently extended to high-energy particle collisions. Experimentally, Bell inequality violations, which challenge Einstein’s principle of local realism, were first observed in low-energy entangled photon systems by A. Aspect, J. F. Clauser, and A. Zeilinger, earning them the 2022 Nobel Prize in Physics. Particle colliders provide a novel setting for probing quantum information theory, operating at energies over 10 orders of magnitude higher than previous experiments and in the presence of electroweak and strong interactions. Additionally, collider detectors offer unique advantages for quantum state reconstruction via quantum state tomography. This book chapter reviews key theoretical and experimental advancements in this emerging field, highlighting its challenges, objectives, and potential impact on both quantum information theory and high-energy physics.
The theoretical concept of photonic quantum nonlocality cannot be implemented physically because of the quantum Rayleigh scattering of single photons. A distinction needs to be made between the correlation of individual, single measurements of pure states and the correlation of the measured ensembles of mixed states. The correlation operator of Pauli vector operators delivers the same probabilities of correlated detections of photons for both independent and multi-photon states as for ‘entangled’ states of photons. As single-photon sources are not needed, the design and implementation of quantum computing operations and other devices will be significantly streamlined.
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by violating Bell inequalities. While the role of entanglement is well studied in the realm of nonrelativistic quantum mechanics, its significance in a relativistic quantum theory is a relatively new field of interest. In this work the consequences of a relativistic description of quantum entanglement are discussed. We analyze the representations of the symmetry groups of special relativity, i.e. of the Lorentz group, and the Poincaré group, on the Hilbert space of states. We describe how unitary, irreducible representations of the Poincaré group for massive spin 1/2 particles are constructed from representations of Wigner's little group. We then proceed to investigate the role of the Wigner rotations in the transformation of quantum states under a change of inertial reference frame. Considering different partitions of the Hilbert space of 2 particles, we find that the entanglement of the quantum states appears different in different inertial frames, depending on the form of the states, the chosen inertial frames, and the particular choice of partition. It is explained, how, despite of this, the maximally possible violation of Bell inequalities is frame independent, when using appropriate spin observables, which are related to the Pauli-Ljubanski vector, a Casimir operator of the Poincaré group.
In quantum mechanics, the general state describing two or more particles is a linear superposition of product states. Such a superposition is called entangled if it cannot be factored into just one product. When only two particles are entangled, the stage is set for Einstein-Podolsky-Rosen (EPR) discussions and Bell's proof that the EPR viewpoint contradicts quantum mechanics. If more than two particles are involved, new possibilities and phenomena arise. For example, the Greenberger, Horne, and Zeilinger (GHZ) disproof of EPR applies. Furthermore, as we point out, with three or more particles even entanglement itself can be an entangled property.