Ancilla-Mediated Higher Entanglement as T-Duality, a Categorial Conjecture
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript by Andrei T. Patrascu explores an ambitious idea of interpreting T-duality in the context of gauge theories and σ-models as a form of higher entanglement, mediated by ancilla fields. The author proposes that these dualities can be understood through the lens of quantum information theory, specifically using a categorial approach that connects quantum circuits with geometric structures in gauge theories. The manuscript is rich in theoretical concepts and aims to bridge multiple advanced fields, including quantum mechanics, gauge theory, category theory, and string theory.
1. The introduction of the manuscript is largely unreferenced, which weakens the foundation of the arguments presented. To strengthen the introduction and provide a more solid context for the discussion, it should be improved by incorporating relevant references in the field such as:
- "Cosmology from string T-duality and zero-point length." The European Physical Journal C 84.7 (2024): 682.
- "The quantum internet: A synergy of quantum information technologies and 6G networks." IET Quantum Communication 4.4 (2023): 147-166.
2. Keywords are missing (please add them)
3. It would be beneficial to include a conceptual figure between the introduction and the lengthy derivation presented in the manuscript. A well-designed figure could visually summarize the key concepts and relationships that are central to the paper, such as the connection between quantum information theory, gauge theories, and T-duality.
4. The analogy between T-duality and quantum entanglement, while intriguing, lacks a formal proof or a detailed mathematical justification. Maybe adding one table to compare the terms could benefit the reader.
5. Poincare invariant Lagrangian (line 310) and other canonical equations should be cited. (line 375, line 488, line 551, line 556 is a bell state, and more)
6. How does the author justify the assumption that non-separability of state spaces, as seen in quantum mechanics, could be a fundamental aspect of any 'quantum' system, and what are the potential implications for physical systems if more general versions of quantum mechanics emerge from new axioms?
Following a thorough revision that addresses this and other points, the manuscript could be recommended for publication.
Comments on the Quality of English LanguageMinor editing of English language required.
Author Response
The introduction of the manuscript is largely unreferenced, which weakens the foundation of the arguments presented. To strengthen the introduction and provide a more solid context for the discussion, it should be improved by incorporating relevant references in the field such as:
- "Cosmology from string T-duality and zero-point length." The European Physical Journal C 84.7 (2024): 682.
- "The quantum internet: A synergy of quantum information technologies and 6G networks." IET Quantum Communication 4.4 (2023): 147-166.
Answer: The references have been added.
Keywords are missing (please add them)
Answer: Keywords have been added
It would be beneficial to include a conceptual figure between the introduction and the lengthy derivation presented in the manuscript. A well-designed figure could visually summarize the key concepts and relationships that are central to the paper, such as the connection between quantum information theory, gauge theories, and T-duality.
Answer: Conceptual figure and relation between the two methods (which can be seen as a table too)
has been added
The analogy between T-duality and quantum entanglement, while intriguing, lacks a formal proof or a detailed mathematical justification. Maybe adding one table to compare the terms could benefit the reader.
Poincare invariant Lagrangian (line 310) and other canonical equations should be cited. (line 375, line 488, line 551, line 556 is a bell state, and more)
Answer: Names of equations have been added
How does the author justify the assumption that non-separability of state spaces, as seen in quantum mechanics, could be a fundamental aspect of any 'quantum' system, and what are the potential implications for physical systems if more general versions of quantum mechanics emerge from new axioms?
Answer: As said in the article, entanglement, and therefore non-separability of states, is a fundamental experimentally observed fact. Future generalisations of quantum mechanics, if done to replicate real natural phenomena, will have to account for them
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper is devoted to ancilla mediated higher entanglements, that are described using category theory approaches. Firstly, author describes basic physical problems connected with special and general relativity, discusses AdS/CFT duality and another questions connected with quantum physics. After that, there is a Lagrangian and the action constructed of it. Also the symmetries are discussed, and gauge transformations are shown. Then author speaks about auxiliary fields and passes to T-duality as a result of higher-entangled state. He shows different wave functions. After that, he passes to the conclusion.
First of all, I don't like the design of the paper. The introduction has the size of about a half of the paper, and it contains a very detailed review of well-known fact. Only in the middle of the paper the author passes to his unique results.
Contrary, the abstract does not give sufficient information about the paper, there are no keywords. Also, the well-known facts are not supported by the links.
In the formulae (7) the integration seems to be incorrect, there is the second differential.
All these problems should be fixed for the publication.
Author Response
First of all, I don't like the design of the paper. The introduction has the size of about a half of the paper, and it contains a very detailed review of well-known fact. Only in the middle of the paper the author passes to his unique results.
Answer: The sections of the paper have been changed, including a part of the previous introduction as a more fitting, new section; Much previously known material has indeed been included for clarity, I hope the re-sectioning of the article makes that more clear.
Contrary, the abstract does not give sufficient information about the paper, there are no keywords. Also, the well-known facts are not supported by the links.
Answer: I updated the abstract
In the formulae (7) the integration seems to be incorrect, there is the second differential.
Answer: I added more citations; I corrected formula 7
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsI think that the paper has been improved. However, the introduction is still quite long, but the redesign of the paper has made it better.
