Consideration of Fidelity for Dynamic of W State in Several Channels With Noise

In quantum information theory, fidelity is a measure of the closeness of the two quantum states. In this work we consider the fidelity for W state in several noisy channels and calculate this parameter for these noisy channels. We showed that the fidelity is approximately equivalent in Pauli channels σ z , σ x ( σ y ) and fidelity for Pauli channels σ x and Pauli channels σ y , are the same. But in depolarizing channel, the fidelity decreases faster than those three channels (Pauli channels σ x , σ y , σ z ). Also, if the system does not interact with the environment, the fidelity stays fixed and at all times is equal to o n e (1). If the interaction between the system and the environment is strong, all the diagrams of fidelity slow down quickly with increasing time.