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

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 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.

arXiv comment6 pages

References in corpus (3)

• On superactivation of zero-error capacities and reversibility of a quantum channel
• Non-commutative graphs based on finite-infinite system couplings: quantum error correction for a qubit coupled to a coherent field
• On errors generated by unitary dynamics of bipartite quantum systems

Cited by in corpus (3)

• On quantum channels generated by covariant positive operator-valued measures on a locally compact group
• Convergence conditions for the quantum relative entropy and other applications of the deneralized quantum Dini lemma
• Compactness criterion for families of quantum operations in the strong convergence topology and its applications