Tomographic Witnessing and Holographic Quantifying of Coherence

TL;DR

This paper introduces a tomographic method for detecting and quantifying quantum coherence, establishing optimal witnesses and a new coherence measure based on the density matrix’s off-diagonal elements.

Contribution

It provides a novel tomographic witnessing technique and a bona fide coherence measure, linking it to existing coherence quantifiers.

Findings

Optimal coherence witness characterized by zero diagonal elements.

New coherence measure based on off-diagonal entries of the density matrix.

Relations established between the new measure and existing coherence measures.

Abstract

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