2013/05/21 by Yichen Huang · 2 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Computing Algorithms and Architecture
paper · doi:10.1109/tit.2013.2257936
openalex publication_date 2013/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04
Entanglement plays a key role in quantum information. The separability problem arises: how to prove that a given quantum state is entangled? Covariance-matrix-based entanglement criteria are the most important and widely used approach to this problem in continuous variable systems. Here, the separability problem is systematically studied in the more experimentally realistic setting that the questioned state is only partly known. A simple general formalism is proposed for this variant of the separability problem. It builds relations between certain classes of criteria and bounds the power of these criteria. In particular, it shows the equivalence of many seemingly different covariance-matrix-based criteria; it offers guidance on the study of and reveals the inherent limitations of covariance-matrix-based criteria. Also, a Shannon entropic criterion is proposed for m ⊕ n-mode states. It unifies and improves many known covariance-matrix-based criteria and Shannon entropic criteria; it is necessary and sufficient for 1 ⊕ n-mode Gaussian states and m ⊕ n-mode bisymmetric Gaussian states.