Symmetry-resolved entanglement detection using partial transpose moments

By A. Neven, J. Carrasco, Vittorio Vitale, C. Kokail, Andreas Elben, Marcello Dalmonte, Pasquale Calabrese, Peter Zoller, B. Vermersch, Richard Kueng and 1 more. npj Quantum Information, 2021

183 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/9281ad1190793e41f7aebd211da32ebdc25e7288

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Citations in the corpus

The randomized measurement toolbox (2022, methodology): “35 have been recently reana-lysed 31,36,40,57 to access other entanglement properties, in particular using the classical shadow framework 36 .”