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

• URL: http://arxiv.org/abs/2403.06733v1
• Date: Mon, 11 Mar 2024 13:55:03 GMT
• Title: On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator
• Authors: G.G. Amosov, A.S. Mokeev, A.N. Pechen
• Abstract summary: We consider error correction based on the theory of non-commutative graphs. We construct a quantum channel generating the non-commutative graph as a linear envelope of the POVM. For this model the quantum anticlique which determines the error correcting subspace has an explicit expression.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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