Abstract
Quantum coherence plays an important role in quantum resource theory, which is strongly related with entanglement. In order to quantify the full coherence of qudit states, we define G-coherence and convex roof of G-coherence, and prove that the G-coherence is a strong coherence monotone and the convex roof of G-coherence is a coherence measure under fully and strictly incoherent operation (FSIO), respectively. Similar to the entanglement factorization law, we prove a coherence factorization law for arbitrary d-dimensional quantum pure and mixed states under FSIO channels, which generalizes the entanglement factorization law for bipartite pure states. Our results will play an important role in the simplification of dynamical coherence measure.
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