Schmidt-Number Detection via Local Randomized Projections with First-Order Moments
A criterion and estimation algorithm for the Schmidt number of a bipartite high-dimensional quantum state that uses local randomized projections (random local unitary and orthogonal rotations drawn from the Haar measure, followed by local observable measurements) and only first-order moments of the outcomes. As the number of random operations grows the criterion approaches the fidelity-based Schmidt-number witness, and it estimates entanglement dimensionality more accurately and with fewer projections than mutually-unbiased-basis and higher-order-moment randomized-measurement methods, demonstrated on maximally entangled states under depolarizing and random noise.
Detecting high-dimensional entanglement by local randomized projections Jin-Min Liang,1 Shuheng
The Schmidt number quantifies the entanglement dimensionality of a bipartite quantum state and is central to high-dimensional quantum information. Conventional detection uses either fixed measurement…