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Liu, Chaobin; Petulante, Nelson

On the von Neumann entropy of certain quantum walks subject to decoherence. (English) Zbl 1204.81107

Math. Struct. Comput. Sci. 20, No. 6, 1099-1115 (2010).
Summary: 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.

Cited in 3 Documents

MSC:

81S22 Open systems, reduced dynamics, master equations, decoherence
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
94A17 Measures of information, entropy
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P15 Quantum measurement theory, state operations, state preparations
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\textit{C. Liu} and \textit{N. Petulante}, Math. Struct. Comput. Sci. 20, No. 6, 1099--1115 (2010; Zbl 1204.81107)
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