Tomographic Witnessing and Holographic Quantifying of Coherence

The detection and quantification of quantum coherence play significant roles in information processing. We present an efficient way tomographic witnessing for both theoretical experimental coherence. prove that a witness is optimal if only all its diagonal elements are zero. Naturally, we obtain bona fide homographic measure given by the sum absolute values real imaginary parts non-diagonal entries density matrix, together with interesting relations other measures like $l_1$ norm robust