Quantum systems in an entangled state  can be used as a primary quantum information channel to perform computational , communicational , metrological [4, 5] and cryptographic tasks that are impossible for classical systems. These possible applications of entangled quantum states stimulate intensive research in the fields of generation and manipulation of them. Entangled states may appear in various systems of interacting quantum particles, such as phonons, ions, electron, nuclear spins, and of a single particle interacting with environment.
We study entanglement between quantum states of multi level spin system of a single particle considering a nucleus with spin 3/2 in both the internal electric field gradient and the external magnetic field. It was shown that entanglement is achieved by applying a magnetic field to a single particle at low temperature ( 5 mK). In this temperature range, the numerical calculation revealed the coincidence between magnetization and concurrence. As a result, the magnetization can be used as an entanglement witness for such systems.
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