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Paper 1
Khovanov homology and quantum error-correcting codes
Rostislav Akhmechet, Milena Harned, Pranav Venkata Konda, Felix Shanglin Liu, Nikhil Mudumbi, Eric Yuang Shao, Zheheng Xiao
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.11252
- arXiv
- 2410.11252
Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections. Audoux used Khovanov homology to define families of quantum error-correcting codes with desirable properties. We explore Khovanov homology and some of its many extensions, namely reduced, annular, and $\mathfrak{sl}_3$ homology, to generate new families of quantum codes and to establish several properties about codes that arise in this way, such as behavior of distance under Reidemeister moves or connected sums.
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Probing quantum correlations in non-degenerate hyper-Raman process
Moumita Das, Biswajit Sen, Ankur Sensharma, Kishore Thapliyal, Anirban Pathak
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04007
- arXiv
- 2410.04007
Possibilities of observing single mode and intermodal quantum correlations (e.g., antibunching, steering and entanglement) are studied for a probed-hyper-Raman system with specific attention on the impact of a probe on the single and multi-mode quantum correlations generated in a hyper-Raman active system. The physical system studied here considers that the probe interacts continuously with the non-degenerate pump modes in the hyper-Raman active system via a nonlinear coupling. The investigation has revealed that quantum correlations in the Raman systems can be controlled using the probe. Further, it is observed that the quantum steering between the pump and anti-Stokes modes can be influenced significantly by controlling the interaction between the system and the probe. Unlike steering, probe could neither deteriorate the nonclassical correlations, namely intermodal entanglement and photon antibunching, nor induce them. Though the witness of the corresponding nonclassical effect depends on the initial state of the probe as well as the coupling strength
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