Symmetry-resolved entanglement detection using partial transpose moments

TL;DR

This paper introduces a set of experimentally feasible criteria based on moments of the partially transposed density operator to detect entanglement in mixed quantum states, with practical measurement strategies and robustness to source drift.

Contribution

It develops a hierarchy of entanglement detection conditions using moments, connecting to the Peres-Horodecki criterion, and provides measurement protocols with confidence intervals.

Findings

First four conditions reliably detect entanglement in various architectures.

Symmetries enhance detection capabilities.

Local random measurements enable estimation with confidence intervals.

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.