2021/03/12 by Antoine Neven, José Carrasco, Jose Carrasco +10 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Eigenvalues and eigenvectors #Mathematics #Moment (physics) #Operator (biology) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum state #Set (abstract data type) #State (computer science) #Statistical physics #Statistics #Symmetry (geometry) #Transpose #Variety (cybernetics) #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1038/s41534-021-00487-y
published as Npj Quantum Inf. 7, 152 (2021) · 11+11 pages, 6 figures
arxiv created 2021/03/12 · openalex publication_date 2021/10/20 · arxiv updated 2022/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k -th condition involves comparing moments of the partially transposed density operator up to order k . Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.