Bound entanglement-assisted prepare-and-measure scenarios

Abstract: We present a class of linear correlation witnesses that can detect bound entanglement in two-ququart Bloch-diagonal states within a three-party prepare-and-measure scenario. We relate the detection power of our witnesses to that of the computable cross norm-realignment (CCNR) criterion. Reliable iterative methods reveal that the separable bound is matched by the classical bound of the correlation witnesses. Several bound entangled states can exceed these bounds, including those with metrological usefulness. In particular, we show that a prominent two-ququart bound entangled state with a positive partial transpose (PPT) can be mixed with up to $40\%$ isotropic noise and still be detected as entangled by our prepare-and-measure witness. Furthermore, our witnesses appear to be experimentally practical, requiring only the use of qubit rotations on Alice's and Bob's sides and product measurements with binary outcomes on Charlie's side.