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Open Quantum Random Walks with Decoherence on Coins with n Degrees of Freedom
Xiong, S Yang, WS
Xiong, S
Yang, WS
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2013-08-01
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10.1007/s10955-013-0772-2
Abstract
In this paper we define a new type of decoherent quantum random walk with parameter 0≤p≤1, which becomes a unitary quantum random walk (UQRW) when p=0 and an open quantum random walk (OQRW) when p=1, respectively. We call this process a partially open quantum random walk (POQRW). We study the limiting distribution of a POQRW on Z 1 subject to decoherence on coins with n degrees of freedom. The limiting distribution of the POQRW converges to a convex combination of normal distributions, under an eigenvalue condition. A Perron-Frobenius type of theorem is established to determine whether or not a POQRW satisfies the eigenvalue condition. Moreover, we explicitly compute the limiting distributions of characteristic equations of the position probability functions when n=2 and 3. © 2013 Springer Science+Business Media New York.
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Journal of Statistical Physics
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