Quantum walk on the line: entanglement and non-local initial conditions

Details Quantum walk on the line: entanglement and non-local initial conditions Quantum walk on the line: entanglement and non-local initial conditions

2005-07-27

arxiv.org/abs/quant-ph/0507264v5

Physical Review A 73, 042302 (2006); Physical Review A 73 069905(E) (2006); Virtual Journal of Quantum Information, 6 issue 4

Physics

Quantum Physics

A few mistakes where corrected. One of them leads to a factor of 2 in eq. (49), the other results remain unchanged. In this ve

Scientific paper

10.1103/PhysRevA.73.042302

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 Neumann entropy of the reduced density operator (entropy of entanglement). In the long time limit, it converges to a well defined value which depends on the initial state. Exact expressions for the asymptotic (long-time) entanglement are obtained for (i) localized initial conditions and (ii) initial conditions in the position subspace spanned by the +1 and -1 position eigenstates.

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