Efficient nonlinear witnessing of non-absolutely separable states with lossy detectors

TL;DR

This paper demonstrates that nonlinear witness operators are more effective than linear ones in detecting non-absolutely separable states, and establishes detector efficiency thresholds to prevent false positives in quantum state identification.

Contribution

It introduces nonlinear witness operators for improved detection of non-absolutely separable states and analyzes detector efficiency thresholds to close detection loopholes.

Findings

Nonlinear witnesses outperform linear ones in identifying non-absolutely separable states.

Critical detector efficiency thresholds are established to prevent false detection.

Examples across various dimensions illustrate the effectiveness of the proposed method.

Abstract

Entangled states are undoubtedly an integral part of various quantum information processing tasks. On the other hand, absolutely separable states which cannot be made entangled under any global unitary operations are useless from the resource theoretic perspective, and hence identifying non-absolutely separable states can be an important issue for designing quantum technologies. Here we report that nonlinear witness operators provide significant improvements in detecting non-absolutely separable states over their linear analogs, by invoking examples of states in various dimensions. We also address the problem of closing detection loophole and find critical efficiency of detectors above which no fake detection of non-absolutely separable (non-absolutely positive partial transposed) states is possible.