1204.1287 (C. M. Chandrashekar et al.)

Decoherence on a two-dimensional quantum walk using four- and two-state
particle    [PDF]

C. M. Chandrashekar, Th. Busch

We study the decoherence of the two-dimensional discrete-time quantum walk evolution using four-state and two-state particles subjected to environmental effects, which lead to state flipping and depolarisation. By evolving the density matrix and measuring the particle-position and $x-y$ spatial entanglement using negativity, we show that the two scheme for quantum walk using two-state particle, with the coin operation and different Pauli basis as translational states are more robust against decoherence than the Grover walk using four-state particle. We also show that the quantum walk symmetries which hold for two-state quantum walk evolution breakdown for the Grover walk adding to various other advantages of using two-state particle over the four-state particle for the two-dimensional quantum walk.

View original: http://arxiv.org/abs/1204.1287