# Weak convergence of complex-valued measure for bi-product path space induced by quantum walk

@article{Konno2012WeakCO, title={Weak convergence of complex-valued measure for bi-product path space induced by quantum walk}, author={Norio Konno and Etsuo Segawa}, journal={arXiv: Mathematical Physics}, year={2012} }

In this paper, a complex-valued measure of bi-product path space induced by quantum walk is presented. In particular, we consider three types of conditional return paths in a power set of the bi-product path space (1) $\Lambda \times \Lambda $, (2) $\Lambda \times \Lambda'$ and (3) $\Lambda'\times \Lambda'$, where $\Lambda$ is the set of all $2n$-length ($n\in \mathbb{N}$) return paths and $\Lambda'(\subseteq \Lambda)$ is the set of all $2n$-length return paths going through $nx$ ($x\in [-1,1… CONTINUE READING

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