Characterizing GME-Dimension through Critical Visibility in Noisy Supersinglet States
(2025) FYSK04 20251Department of Physics
Mathematical Physics
- Abstract
- Entanglement in quantum mechanics manifests in two distinct forms, either between many qubit systems or two high-dimensional quantum systems with entangled degrees of freedom. These two classifications are well established. However, recent strides have been made to unify these two conditions as quantum technologies evolve further. The GME-dimension quantifies the entangled degrees of freedom in a multiparticle system.
In this work, we investigate the noise-robustness of the totally antisymmetric supersinglet state, developing criteria to estimate the maximum tolerated noise before its GME-dimension is reduced. We propose methods based on fidelity bounds and convex programming, and compare the noise robustness of the supersingle state... (More) - Entanglement in quantum mechanics manifests in two distinct forms, either between many qubit systems or two high-dimensional quantum systems with entangled degrees of freedom. These two classifications are well established. However, recent strides have been made to unify these two conditions as quantum technologies evolve further. The GME-dimension quantifies the entangled degrees of freedom in a multiparticle system.
In this work, we investigate the noise-robustness of the totally antisymmetric supersinglet state, developing criteria to estimate the maximum tolerated noise before its GME-dimension is reduced. We propose methods based on fidelity bounds and convex programming, and compare the noise robustness of the supersingle state to the GHZ and Cluster states. (Less) - Popular Abstract
- Albert Einstein is considered by many to be one of the smartest men to have ever lived. But at the dawn of quantum mechanics, he stood in strong opposition to it. Of course, he still believed in quantum mechanics, and in fact, his Nobel Prize was not for his famous equation E=mc^2 or for general relativity. It was his paper on the photoelectric effect, a purely quantum mechanical phenomenon, that earned him this honor. His issue with quantum mechanics was the "spooky action at a distance" phenomenon, as Einstein famously called it. This phenomenon was later given the name "Verschränkung" which is German for entanglement, by Erwin Schrödinger, whose cat is equally famous as he. Entanglement is the phenomenon where, once two particles have... (More)
- Albert Einstein is considered by many to be one of the smartest men to have ever lived. But at the dawn of quantum mechanics, he stood in strong opposition to it. Of course, he still believed in quantum mechanics, and in fact, his Nobel Prize was not for his famous equation E=mc^2 or for general relativity. It was his paper on the photoelectric effect, a purely quantum mechanical phenomenon, that earned him this honor. His issue with quantum mechanics was the "spooky action at a distance" phenomenon, as Einstein famously called it. This phenomenon was later given the name "Verschränkung" which is German for entanglement, by Erwin Schrödinger, whose cat is equally famous as he. Entanglement is the phenomenon where, once two particles have interacted, they can no longer be described as independent particles. This means that they can be light-years away from each other, but once you interact with one particle, the other one will instantly react to the changes to the first particle.
In the modern era, quantum mechanics and all of its phenomena belong to an elite class of some of the most tested and proven theories. Unlike in the days of Einstein, we no longer ask the question, "is entanglement real"?, but instead wonder what its nature is and what its use is. Turns out, physicists have shown that entanglement is crucial in achieving quantum computers powerful enough to outperform classical machines, a milestone known as quantum supremacy. Just as digital computers revolutionized the world we live in, quantum supremacy aims to do the same. Increasing our computing power via quantum computers would drastically help in fields such as medicine and material science. One could model how medicine affects the body before giving it to patients, or model how a material handles stress, heat, etc, without putting the material through a series of tests.
However, two problems persist. We know how to deal with entanglement between many simple two-dimensional particles, often called a qubit. We also know how to deal with the entanglement of two particles that have many dimensions. However, classification of entanglement involving many particles and many dimensions was only done recently. Being able to classify and use the entanglement in high-dimensional multi-particle systems could drastically increase the efficiency of quantum computers, bringing us closer to true quantum supremacy. The second problem is that quantum mechanical systems are very fragile. Introducing noise to the system can de-cohere the system, removing all the nice quantum mechanical effects we want. Therefore, we would like to find what entangled system that is high-dimensional and multi-particle is the most noise robust, as it could be the key to reaching quantum supremacy. That is the focus of this paper. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9202635
- author
- Modaresi, Poya LU
- supervisor
- organization
- course
- FYSK04 20251
- year
- 2025
- type
- M2 - Bachelor Degree
- subject
- keywords
- Entanglement, Genuine-Multipartite-Entanglement, GME-dimension, Supersinglets
- language
- English
- id
- 9202635
- date added to LUP
- 2025-06-24 08:27:31
- date last changed
- 2025-06-24 08:27:31
@misc{9202635,
abstract = {{Entanglement in quantum mechanics manifests in two distinct forms, either between many qubit systems or two high-dimensional quantum systems with entangled degrees of freedom. These two classifications are well established. However, recent strides have been made to unify these two conditions as quantum technologies evolve further. The GME-dimension quantifies the entangled degrees of freedom in a multiparticle system.
In this work, we investigate the noise-robustness of the totally antisymmetric supersinglet state, developing criteria to estimate the maximum tolerated noise before its GME-dimension is reduced. We propose methods based on fidelity bounds and convex programming, and compare the noise robustness of the supersingle state to the GHZ and Cluster states.}},
author = {{Modaresi, Poya}},
language = {{eng}},
note = {{Student Paper}},
title = {{Characterizing GME-Dimension through Critical Visibility in Noisy Supersinglet States}},
year = {{2025}},
}