Operational detection of entanglement via quantum designs

TL;DR

This paper introduces new entanglement detection criteria based on quantum designs, revealing that SIC POVMs are as effective as more complex measurements, and highlights their fundamental role in quantum information processing.

Contribution

The paper develops entanglement detection criteria using quantum designs, showing equivalence between criteria with different settings and emphasizing the importance of SIC POVMs.

Findings

Criteria with more settings are equivalent to minimal SIC POVM-based criteria.

SIC POVMs play a potentially unique role in quantum information processing.

Nonlinear criteria are not always superior to linear ones for entanglement detection.

Abstract

From an operational point of view, we propose several new entanglement detection criteria using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria with more settings are exactly equivalent to the corresponding ones with the minimal number of settings, namely the symmetric informationally complete positive operator-valued measures (SIC POVMs). Fundamentally, this observation highlights the potentially unique role played by SIC POVMs in quantum information processing. Experimentally, this provides the minimal number of settings that one should choose for detecting entanglement. Furthermore, we find that nonlinear criteria are not always better than linear ones for the task of entanglement detection.