State-witness contraction

TL;DR

This paper develops methods to construct and optimize entanglement witnesses, including for multipartite and undistillable states, improving detection capabilities and experimental feasibility with randomized measurements.

Contribution

It introduces new techniques for constructing and optimizing both linear and nonlinear entanglement witnesses, enhancing detection of complex entangled states and distillability properties.

Findings

Constructed new linear and nonlinear entanglement witnesses.

Improved existing trace polynomial witnesses while maintaining symmetry.

Developed efficient optimization methods for multicopy witnesses.

Abstract

We construct both nonlinear and linear entanglement witnesses, by tensoring and partial tracing existing states and witnesses. We show that little shared quantum resources allow to employ decomposable witnesses to obtain larger ones detecting locally undistillable states, and find analytic witnesses for multipartite entangled states that are undistillable across all bipartitions. Crucially, we show how to efficiently optimize multicopy witnesses to desired states, which is a current challenge. As an example of both theoretical and experimental interest, existing trace polynomial witnesses are significantly improved while preserving their symmetries and implementability with randomized measurements. Besides detecting entanglement, we also find new witnesses detecting $k$-copy distillability. A recipe for the single-copy case is shown to be effective for generic and Werner states.