An algorithm to explore entanglement in small systems

Robin Reuvers

Published 2017-11-21Version 1

A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to numerically find pure states that maximize Schmidt norms, potentially minimizing or maximizing entanglement across several bipartite cuts at the same time, possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we ask how this algorithm can help to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels.