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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.20983 |
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| _version_ | 1866914117245206528 |
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| author | Floratos, Emmanuel Manolas, Kimon Tsohantjis, Ioannis |
| author_facet | Floratos, Emmanuel Manolas, Kimon Tsohantjis, Ioannis |
| contents | Unitary metaplectic representations of the group $SL_2(\mathbb{Z}_{2^n})$ are necessary to describe the evolution of $2^n$-dimensional quantum systems, such as systems involving $n$ qubits. It is shown that in order for the metaplectic property to be fulfilled, an increase in the dimensionality of the involved $n$-qubit Hilbert spaces, from $2^n$ to $2^{2n}$, is necessary. Thus we construct the general matrix form of such representations based on the magnetic translations of the diagonal subgroup $HW_{2^n} \otimes HW_{2^n}$. Comparisson with other approaches on this problem of the literature are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of Metaplectic Representations of $SL_2(\mathbb{Z}_{2^n})$ and Twisted Magnetic Translations Floratos, Emmanuel Manolas, Kimon Tsohantjis, Ioannis Quantum Physics High Energy Physics - Theory Mathematical Physics Unitary metaplectic representations of the group $SL_2(\mathbb{Z}_{2^n})$ are necessary to describe the evolution of $2^n$-dimensional quantum systems, such as systems involving $n$ qubits. It is shown that in order for the metaplectic property to be fulfilled, an increase in the dimensionality of the involved $n$-qubit Hilbert spaces, from $2^n$ to $2^{2n}$, is necessary. Thus we construct the general matrix form of such representations based on the magnetic translations of the diagonal subgroup $HW_{2^n} \otimes HW_{2^n}$. Comparisson with other approaches on this problem of the literature are discussed. |
| title | Construction of Metaplectic Representations of $SL_2(\mathbb{Z}_{2^n})$ and Twisted Magnetic Translations |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2505.20983 |