School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
Centre for Quantum Software and Information, School of Software, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia.
Phys Rev Lett. 2018 Jul 6;121(1):010401. doi: 10.1103/PhysRevLett.121.010401.
We characterize the distillation of quantum coherence in the one-shot setting, that is, the conversion of general quantum states into maximally coherent states under different classes of quantum operations. We show that the maximally incoherent operations (MIO) and the dephasing-covariant incoherent operations (DIO) have the same power in the task of one-shot coherence distillation. We establish that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which we show to correspond to a quantum hypothesis testing problem. Further, we introduce a family of coherence monotones generalizing the robustness of coherence as well as the modified trace distance of coherence, and show that they admit an operational interpretation in characterizing the fidelity of distillation under different classes of operations. By providing an explicit formula for these quantities for pure states, we show that the one-shot distillable coherence under MIO, DIO, strictly incoherent operations, and incoherent operations is equal for all pure states.
我们描述了单次量子相干蒸馏，即在不同量子操作类下将一般量子态转换为最大相干态。我们表明，最大非相干操作（MIO）和相位退协变非相干操作（DIO）在单次相干蒸馏任务中具有相同的能力。我们证明了在 MIO 和 DIO 下的单次可蒸馏相干性可以通过半定规划有效地计算，这与量子假设检验问题相对应。进一步，我们引入了一类相干单调函数，它们推广了相干的稳健性和相干的修改迹距离，并表明它们在不同操作类下的保真度的描述中具有操作解释。通过为纯态提供这些量的显式公式，我们表明对于所有纯态，MIO、DIO、严格非相干操作和非相干操作下的单次可蒸馏相干性是相等的。
