Tomographic Witnessing and Holographic Quantifying of Coherence

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.

arXiv comment8 pages, close to published version

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Cited by in corpus (5)

• Common Coherence Witnesses and Common Coherent States
• Device-independent Verification of Quantum Coherence without Quantum Control
• Witnessing quantum coherence with prior knowledge of observables
• Detecting coherence with respect to general quantum measurements
• Classifying coherence with a finite set of witnesses