On the von Neumann entropy of certain quantum walks subject to decoherence

Details On the von Neumann entropy of certain quantum walks subject to decoherence On the von Neumann entropy of certain quantum walks subject to decoherence

2010-07-19

arxiv.org/abs/1007.3057v1

Math. Struct. in Comp. Science (2010), vol. 20, pp. 1099-1115

Physics

Quantum Physics

Scientific paper

Consider a discrete-time quantum walk on the $N$-cycle governed by the following condition: at every time step of the walk, the option persists, with probability $p$, of exercising a projective measurement on the coin degree of freedom. For a bipartite quantum system of this kind, we prove that the von Neumann entropy of the total density operator converges to its maximum value. Thus, when influenced by decoherence, the mutual information between the two subsystems, corresponding respectively to the space of the coin and the space of the walker, eventually must diminish to zero. To put it plainly, any level of decoherence greater than zero forces the system eventually to become completely "disentangled".}

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