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
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Random Walks in One Dimension
Quantum Information Processing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Quantum Walks for Computer Scientists
Quantum Walks for Computer Scientists
On the von neumann entropy of certain quantum walks subject to decoherence†
Mathematical Structures in Computer Science
Maximal entanglement from quantum random walks
Quantum Information Processing
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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The discrete-time quantum walk is a quantum counterpart of the random walk. It is expected that the model plays important roles in the quantum field. In the quantum information theory, entanglement is a key resource. We use the von Neumann entropy to measure the entanglement between the coin and the particle's position of the quantum walks. Also we deal with the Shannon entropy which is an important quantity in the information theory. In this paper, we show limits of the von Neumann entropy and the Shannon entropy of the quantum walks on the one dimensional lattice starting from the origin defined by arbitrary coin and initial state. In order to derive these limits, we use the path counting method which is a combinatorial method for computing probability amplitude.