Mathematical framework for detection and quantification of nonclassical correlation
Abstract
Existing measures of bipartite nonclassical correlation that is typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps. The class is in analogy to the class of positive-but-not-completely-positive (PnCP) maps that have been commonly used in the entanglement theories. Linear and nonlinear EnCE maps are investigated. We also prove subadditivity of the measures in a form of logarithmic fidelity.
Cite
@article{arxiv.0802.2263,
title = {Mathematical framework for detection and quantification of nonclassical correlation},
author = {Akira SaiToh and Robabeh Rahimi and Mikio Nakahara},
journal= {arXiv preprint arXiv:0802.2263},
year = {2010}
}
Comments
14 pages, no figure, v1-v2: 4 pages, v2: a proposition and a proof corrected, v3: 6 pages, more details of proofs written, an explanation of a measure corrected, v4: 15 pages, a new nonlinear EnCE map introduced, v5: 15 pages, typos corrected, v6: 18 pages, an inconsistent remark removed, v7: 19 pages, minor changes in presentation, v8-v10: 14 pages, minor revisions, to appear in QIC