Deterministic Coherence Distillation

Coherence distillation is one of the central problems in the resource theory of coherence. In this Letter, we complete the deterministic distillation of quantum coherence for a finite number of coherent states under strictly incoherent operations. Specifically, we find the necessary and sufficient condition for the transformation from a mixed coherent state into a pure state via strictly incoherent operations, which recovers a connection between the resource theory of coherence and the algebraic theory of majorization lattice. With the help of this condition, we present the deterministic coherence distillation scheme and derive the maximum number of maximally coherent states obtained via this scheme.

Figure 1

Schematic picture of the deterministic coherence transformation via strictly incoherent operations. Here, ${\mathrm{\Pi }}_{\alpha }={\mathbb{P}}_{\alpha }·{\mathbb{P}}_{\alpha }$ for incoherent projective operator ${\mathbb{P}}_{\alpha }$, $\psi (\mathcal{S})$ is the pure coherent state determined by $\vee \mathcal{S}$, ${\tilde{\mathrm{\Lambda }}}_{\alpha }$ are the strictly incoherent operations such that ${\tilde{\mathrm{\Lambda }}}_{\alpha }({\psi }_{\alpha })=\psi$, $\overline{\mathrm{\Lambda }}$ is the strictly incoherent operation such that $\overline{\mathrm{\Lambda }}(\psi )=\phi$, and all the others are the same as in the main text.