Symmetry-resolved entanglement detection using partial transpose moments

• Published in: npj quantum information Vol. 7; no. 1; pp. 1 - 12
• Main Authors: Neven, Antoine, Carrasco, Jose, Vitale, Vittorio, Kokail, Christian, Elben, Andreas, Dalmonte, Marcello, Calabrese, Pasquale, Zoller, Peter, Vermersch, Benoȋt, Kueng, Richard, Kraus, Barbara
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 20-10-2021; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/119; 639/766/483/481; Classical and Quantum Gravitation; Physics; Physics and Astronomy; Quantum Computing; Quantum Field Theories; Quantum Information Technology; Quantum Physics; Relativity Theory; Spintronics; String Theory; Symmetry; Theoretical physics
• ISSN: 2056-6387; 2056-6387
• DOI: 10.1038/s41534-021-00487-y

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.