Abstract
The time-evolution of the trace distance between two qubit states in the presence of an initial correlation with an environment is investigated by means of the exactly solvable model of qubit and environmental system, where there is at most one excitation in the whole system, It is found that the trace distance can exceed its initial value during the time-evolution under certain conditions if the qubit is initially entangled with the environment. Furthermore the Bures distance between two qubit states is investigated. It is seen that the time-evolution of the Bures distance is quite different from that of the trace distance.
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