STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Quantum Walks for Computer Scientists
Quantum Walks for Computer Scientists
Entanglement for discrete-time quantum walks on the line
Quantum Information & Computation
Quantum walks: a comprehensive review
Quantum Information Processing
Limit theorems for the interference terms of discrete-time quantum walks on the line
Quantum Information & Computation
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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.