Improved entanglement detection with subspace witnesses

TL;DR

This paper introduces a subspace entanglement witness that detects a broader class of entangled states more robustly and efficiently than traditional fidelity-based methods, demonstrated experimentally on a two-qubit diamond system.

Contribution

The paper proposes a novel subspace witness for entanglement detection that outperforms conventional fidelity-based witnesses in robustness and efficiency, extending to multipartite states.

Findings

Subspace witness detects a broader class of entangled states.

Experimental validation on a two-qubit diamond system.

Facilitates lower-bound quantification of entanglement.

Abstract

Entanglement, while being critical in many quantum applications, is difficult to characterize experimentally. While entanglement witnesses based on the fidelity to the target entangled state are efficient detectors of entanglement, they in general underestimate the amount of entanglement due to errors during state preparation and measurement. Therefore, to detect entanglement more robustly in the presence of such control errors, we introduce a 'subspace' witness that detects a broader class of entangled states with strictly larger violation than the conventional state-fidelity witness at the cost of additional measurements, while remaining more efficient with respect to state tomography. We experimentally demonstrate the advantages of the subspace witness by generating and detecting entanglement with a hybrid, two-qubit system composed of electronic spins in diamond. We further extend the notion of subspace witness to specific genuine multipartite entangled (GME) states such as GHZ, W, and Dicke states, and motivate the choice of the metric based on quantum information tasks such as entanglement-enhanced sensing. In addition, as the subspace witness identifies the many-body coherences of the target entangled state, it facilitates (beyond detection) lower-bound quantification of entanglement via generalized concurrences. We expect the straightforward and efficient implementation of subspace witnesses would be beneficial in detecting specific GME states in noisy, intermediate-scale quantum processors with a hundred qubits.