Investigation of a Two-Qubit Decoherence by Using Bloch Vectors

The loss of the coherence happens due to the interaction between the desired system and its surroundings. Addressing decoherence is one of the main concepts in the study of quantum channels to access their potential for various scale. In this process the information of the system is penetrated into the environment. Therefore, the measurement of the environment could be used as the error correction method. Phase damping channels principally belong to random unitary channels and can be corrected by classical information. This paper presents a method to generate non-random unitary phase damping channels based on the Bloch vectors in two qubits systems. A phase damping channel which consisted of a two qubits system and a single qubit environment was investigated. The results demonstrated that the phase damping channels belong to random unitary dynamics if the three-dimensional tetrahedron volume spanned by the Bloch vectors in $ℝ^3$ is not zero, or, the same hyperplane in $ℝ^3$ was not pointed by the Bloch vectors. It is found that the Bell state belongs to random unitary class and can be corrected based on classical information obtained from environmental measurements.