Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages

TL;DR

This paper introduces linear correlation witnesses for detecting bound entanglement in four-dimensional quantum messages within a three-party prepare-and-measure setup, demonstrating their effectiveness and experimental practicality.

Contribution

It develops a new class of correlation witnesses for bound entanglement detection in four-dimensional quantum systems, linking their power to the CCNR criterion and showing experimental feasibility.

Findings

Can detect bound entangled states with up to 40% isotropic noise

Witnesses are practical, requiring only simple qubit rotations and binary measurements

Effective for high-dimensional bound entangled states, including PPT states

Abstract

We present a class of linear correlation witnesses that detects bound entanglement within a three-party prepare-and-measure scenario with four-dimensional quantum messages. We relate the detection power of our witnesses for two-ququart Bloch-product-diagonal states to that of the computable cross norm-realignment (CCNR) criterion. Several bound entangled states in four or even higher dimensions, including those which are useful in metrology, can exceed the separable bound computed by reliable iterative methods. 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 qubit measurements with binary outcomes on Charlie's side.