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arXiv · 2403.06733

On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator

G. G. Amosov·A. S. Mokeev·A. N. Pechen
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Abstract

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 Schr\"odinger 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.

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G. G. Amosov, A. S. Mokeev, A. N. Pechen. 2024-03-11. On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator. https://doi.org/10.1134/s1995080221100036

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