Teleportation-based filtering for gravitational-wave detectors

Employing the principle of quantum teleportation in gravitational-wave detectors provides a method to address technical challenges associated with implementing quantum filters for squeezed-light injection. A recent proposal has shown that an arbitrary number of effective squeezing-angle rotations can be achieved by cascading quantum teleportation, yielding sensitivity equivalent to frequency-dependent pre-filtering. A natural question is whether the teleportation-based protocol can also realize frequency-dependent post-filtering. In this work, we examine this possibility and show that, with perfect teleportation fidelity, post-filtering can be fully implemented. In practice, however, various imperfections make the sensitivity nearly equivalent to that of teleportation-based pre-filtering. We apply this scheme to the low-frequency detector in the Einstein Telescope xylophone configuration and find that teleportation-based post-filtering could also be a candidate for the detector's design.