Entanglement as the cross-symmetric part of quantum discord

We show that a large class of discord measures can be used to construct entanglement monotones, by proving that the minimal discord over all cross-symmetric state extensions is non-increasing under local operations and classical communications (LOCC). In particular, the result implies that the coherence measure can be used to quantify entanglement since for each coherence measure, the corresponding correlated coherence can be also regarded as a kind of discord. It is well known that the Hilbert -Schmidt distance is not suitable for quantifying entanglement since it is not contractive under quantum operations. At last, the results presented here show that the corresponding entanglement quantifier defined with the Hilbert-Schmidt distance is non-increasing under LOCC, which refutes a long-held but unstated convention that only contractive distances can be used to construct entanglement monotones.& COPY; 2023 Elsevier B.V. All rights reserved.