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Dynamics of entanglement in qubit-qutrit with x component of DM interaction

In this present paper we study the entanglement dynamics in qubit A-qutrit B pair under x component of Dzyaloshinshkii-Moriya $(D_{x})$ by taking an auxiliary qubit C. Here we consider an entangled qubit-qutrit pair initially prepared in two parameter qubit-qutrit states and one auxiliary qubit prepared in pure state interacts with the qutrit of the pair through DM interaction. We trace away the auxiliary qubit and calculate the reduced dynamics in qubit A-qutrit B pair to study the influence of the state of auxiliary qubit C and $D_{x}$ on entanglement. We find that the state (probability amplitude) of auxiliary qubit does not influence the entanglement, only $D_{x}$ influences the same. The phenomenon of entanglement sudden death (ESD) induced by $D_{x}$ has also been observed. We also present the affected and unaffected two parameter qubit-qutrit states by $D_{x}$.