Operational Detection of Entanglement via Quantum Designs

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.

The entanglement criteria based on equiangular tight frames

“…Jivulescu et al proposed a class of entanglement criteria via projective tensor norms [15]. In 2022, Yan et al proposed several entanglement detection criteria using quantum designs [16]. Recently, we proposed a family of separability criteria and presented lower bounds of concurrence and the convex-roof extended negativity for arbitrary dimensional systems [17].…”

“…Assume ρ ABC is a tripartite fully separable state and M = [m ijk ] is the hypermatrix defined in(16), next let Y nA×nB×nC = [y ijk ] be an arbitrary hypermatrix, then…”