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

Published online by Cambridge University Press:  08 November 2010

CHAOBIN LIU  and
NELSON PETULANTE
CHAOBIN LIU
Affiliation:
Department of Mathematics, Bowie State University, 14000 Jericho Park Road, Bowie, Maryland 20715, U.S.A. Email: cliu@bowiestate.edu, npetulante@bowiestate.edu
NELSON PETULANTE
Affiliation:
Department of Mathematics, Bowie State University, 14000 Jericho Park Road, Bowie, Maryland 20715, U.S.A. Email: cliu@bowiestate.edu, npetulante@bowiestate.edu
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Abstract

In this paper, we consider a discrete-time quantum walk on the N-cycle governed by the condition that 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 to the space of the coin and the space of the walker must eventually diminish to zero. Put plainly, any level of decoherence greater than zero forces the system to become completely ‘disentangled’ eventually.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Special Issue 6: Quantum Algorithms , December 2010 , pp. 1099 - 1115
Copyright
Copyright © Cambridge University Press 2010

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