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One-Shot Coherence Distillation

Regula, Bartosz; Fang, Kun; Wang, Xin; Adesso, Gerardo

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Authors

Bartosz Regula

Kun Fang

Xin Wang



Abstract

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.

Journal Article Type Article
Acceptance Date Apr 18, 2018
Online Publication Date Jul 3, 2018
Publication Date Jul 6, 2018
Deposit Date Jul 6, 2018
Publicly Available Date Jul 6, 2018
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 121
Issue 1
DOI https://doi.org/10.1103/PhysRevLett.121.010401
Public URL https://nottingham-repository.worktribe.com/output/945618
Publisher URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.010401#fulltext

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