Wigner function analysis of the decoherence of adiscrete-time quantum walk in the bit-phase noisechannel

The one-dimensional discrete-time Hadamard quantum walk in the bit-phase noise channel is studied using the Wigner function. Decoherence is characterized using the l1-norm of coherence, Wigner function, and complex Wigner entropy. The l1-norm of coherence is used to quantify the persistence of coin coherence, and the non-classicality is verified through negativity of the Wigner function. Analysis of the complex Wigner entropy revealed a non-monotonic behavior in the non-classicality of the quantum walk, with an optimal noise level where the non-classicality is maximized. The Wigner function analysis is able to provide information related to non-classicality that is not possible using the standard Hilbert-space operator formalism.