2005/07/31 by G. Abal, R. Siri, A. Romanelli +1
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1103/physreva.73.042302
published as Physical Review A 73, 042302 (2006); Physical Review A 73 069905(E) (2006); Virtual Journal of Quantum Information, 6 issue 4 (2006) · A few mistakes where corrected. One of them leads to a factor of 2 in eq. (49), the other results remain unchanged. In this version, several figures where replaced by color versions
openalex publication_date 2006/04/04 · arxiv created 2008/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumman entropy of the reduced density operator (entropy of entanglement). We show analytically that for a Hadamard walk with local initial conditions the asymptotic entanglement is 0.872 for all initial coin states. When nonlocal initial conditions are considered, the asymptotic entanglement varies smoothly between almost complete entanglement and no entanglement (product state). An exact expression for the asymptotic (long-time) entanglement is obtained for initial conditions in the position subspace spanned by \ensuremath|\ifmmode±\else\textpm\fi1⟩.