Interrelation between partial coherence and quantum correlations

Both coherence and entanglement stem from the superposition principle, capture quantumness of a physical system, and play a central role in quantum physics. In a multipartite quantum system, coherence and quantum correlations are closely connected. In particular, it has been established that quantum coherence of a bipartite state is an important resource for its conversion to entanglement [A. Streltsov et al., Phys. Rev. Lett. 115, 020403 (2015)] and to quantum discord [J. Ma et al., Phys. Rev. Lett. 116, 160407 (2016)]. We show here that there is a very close association between partial coherence introduced by Luo and Sun [S. Luo and Y. Sun, Phys. Rev. A 96, 022136 (2017)] and quantum correlations (quantified by quantum discord) in both directions. Furthermore, we propose families of coherence measures in terms of quantum correlations and quantum Fisher information.

Figure 1

(a) Partial incoherent operations cannot generate quantum correlations from partial incoherent input states of quantum system ${\mathcal{H}}^a\otimes {\mathcal{H}}^b$. (b) On the contrary, if the input state is partial coherent, the partial coherence can be transformed into quantum correlations via partial incoherent operations. However, the amount of quantum correlations generated from partial coherence does not exceed the amount of the original partial coherence.

Figure 2

(a) Nonzero-discord states are in themselves partial coherent states and the partial coherence does not disappear via any local unitary operations on parties $a$ and $b$. (b) On the contrary, a zero-discord state itself is partial incoherent state or there exists a local unitary operation that causes the partial coherence to vanish.