Polynomial representation for multipartite entanglement of resonating valence bond ladders

TL;DR

This paper introduces a polynomial method to analyze multipartite entanglement in resonating valence bond (RVB) states on ladder lattices, demonstrating their genuine multipartite entanglement and applicability to doped and superposed RVB states.

Contribution

A novel polynomial representation for multipartite quantum states enabling proof of entanglement properties in RVB states on ladder lattices.

Findings

RVB states on ladder lattices have genuine multipartite entanglement.

The polynomial technique detects entanglement in doped and superposed RVB states.

The method applies to various superpositions of singlet coverings.

Abstract

A resonating valence bond (RVB) state of a lattice of quantum systems is a potential resource for quantum computing and communicating devices. It is a superposition of singlet, i.e., dimer, coverings - often restricted to nearest-neighbour ones - of the lattice. We develop a polynomial representation of multipartite quantum states to prove that RVB states on ladder lattices possess genuine multipartite entanglement. The multipartite entanglement of doped RVB states and RVB states that are superposed with varying weights for singlet coverings of ladder lattices can both be detected by using this technique.