Entanglement witnesses for stabilizer states and subspaces beyond qubits

TL;DR

This paper develops new entanglement witnesses for multipartite stabilizer states and subspaces, including graph states of arbitrary local dimension, enhancing detection robustness in higher-dimensional quantum systems.

Contribution

It generalizes previous witness constructions to multi-qudit stabilizer states and graph states, improving noise robustness in entanglement detection.

Findings

Witnesses are effective for entangled subspaces from multi-qudit stabilizer formalism.

Constructed witnesses include graph states of arbitrary local dimension.

Witnesses show superior noise robustness in higher-dimensional systems.

Abstract

Genuine multipartite entanglement is arguably the most valuable form of entanglement in the multipartite case, with applications, for instance, in quantum metrology. In order to detect that form of entanglement in multipartite quantum states, one typically uses entanglement witnesses. The aim of this paper is to generalize the results of [G. T\'oth and O. G\"uhne, Phys. Rev. A \textbf{72}, 022340 (2005)] in order to provide a construction of witnesses of genuine multipartite entanglement tailored to entangled subspaces originating from the \textit{multi-qudit} stabilizer formalism -- a framework well known for its role in quantum error correction, which also provides a very convenient description of a broad class of entangled multipartite states (both pure and mixed). Our construction includes graph states of arbitrary local dimension. We then show that in certain situations, the obtained witnesses detecting genuine multipartite entanglement in quantum systems of higher local dimension are superior in terms of noise robustness to those derived for multiqubit states.