Asymptotic evolution of quantum walks on the N-cycle subject to decoherence on both the coin and position degrees of freedom
- Department of Mathematics, Bowie State University, Bowie, Maryland 20715 (United States)
Consider a discrete-time quantum walk on the N-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some conclusions about the asymptotic behavior of the system. When N is odd, the density matrix of the system tends, in the long run, to the maximally mixed state, independent of the initial state. When N is even, although the behavior of the system is not necessarily asymptotically stationary, in this case too an explicit formulation is obtained of the asymptotic dynamics of the system. Moreover, this approach enables us to specify the limiting behavior of the mutual information, viewed as a measure of quantum entanglement between subsystems (coin and walker). In particular, our results provide efficient theoretical confirmation of the findings of previous authors, who have arrived at their results through extensive numerical simulations. Our results can be attributed to an important theorem which, for a generalized random unitary operation, explicitly identifies the structure of all of its eigenspaces corresponding to eigenvalues of unit modulus.
- OSTI ID:
- 22038623
- Journal Information:
- Physical Review. A, Vol. 84, Issue 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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