Entanglement criteria and bound entanglement identification via local random unitaries

Abstract

The characterization of high-dimensional states is important for quantum information processing. Here, we propose both linear and nonlinear entanglement criteria for states with unequal local dimensions and show that they offer complementary detection capabilities. These entanglement criteria are further generalized to tripartite systems by analyzing all possible bipartitions. Finally, we introduce a certification protocol based on classical shadows to identify whether a confirmed entangled state is indeed a bound state by verifying invariance under partial transposition. Numerical simulations successfully confirm the effectiveness of the proposed results.