The coin-position entanglement generated by the evolution operator of a discrete–time quantum walk is quantified, using the von Neumann entropy of the reduced density operator (entropy of entanglement). In the case of a single walker, the entropy of entanglement converges, in the long time limit, to a well defined value which depends on the initial state. Exact expressions are obtained for loca...

Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications optimization. We study the question of certifying signomials based on recently proposed approach Sums-of-AM/GM-Exponentials (SAGE) decomposition due to second author and Shah. The existence SAGE sufficient condition for signomial, it can be verified by solving tractable c...