On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917929994420224 |
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| author | Amosov, G. G. Mokeev, A. S. Pechen, A. N. |
| author_facet | Amosov, G. G. Mokeev, A. S. Pechen, A. N. |
| contents | We consider error correction, based on the theory of non-commutative graphs, for a model of a qubit interacting with quantum oscillator. The dynamics of the composite system is governed by the Schrödinger equation which generates positive operator-valued measure (POVM) for the system dynamics. We construct a quantum channel generating the non-commutative graph as a linear envelope of the POVM. The idea is based on applying a generalized version of a quantum channel using the apparatus of von Neumann algebras. The results are analyzes for a non-commutative graph generated by a qubit interacting with quantum oscillator. For this model the quantum anticlique which determines the error correcting subspace has an explicit expression. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06733 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator Amosov, G. G. Mokeev, A. S. Pechen, A. N. Quantum Physics Mathematical Physics We consider error correction, based on the theory of non-commutative graphs, for a model of a qubit interacting with quantum oscillator. The dynamics of the composite system is governed by the Schrödinger equation which generates positive operator-valued measure (POVM) for the system dynamics. We construct a quantum channel generating the non-commutative graph as a linear envelope of the POVM. The idea is based on applying a generalized version of a quantum channel using the apparatus of von Neumann algebras. The results are analyzes for a non-commutative graph generated by a qubit interacting with quantum oscillator. For this model the quantum anticlique which determines the error correcting subspace has an explicit expression. |
| title | On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.06733 |