Bosonic interference as a complementary resource for implementation of quantum walks
Magdalena Stobińska, Peter P. Rohde, Paweł Kurzyński · arXiv (Cornell University) · 2015
Quantum walks are interesting simple models for describing various fundamental processes in nature ranging from chaos or photosynthesis to universal quantum computation. Their implementation usually comprises a single particle and $O(n^2)$ optical elements, where $n$ is the size of the quantum walk space. The question arises if this can be achieved with fewer or complementary resources. Here we show that this can be done using a multi-particle Hong--Ou--Mandel interference. It employs $O(n)$ indistinguishable bosons and a single beam splitter to achieve a similar quantum walk. In addition we show that a quantum-to-classical transition takes place if the particles become distinguishable. This approach establishes a link between the fundamental indistinguishability of quantum particles and the wavelike coherent nature of the walk.