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Generic bound coherence under strictly incoherent operations

Lami, Ludovico; Regula, Bartosz; Adesso, Gerardo


Ludovico Lami

Bartosz Regula


We compute analytically the maximal rates of distillation of quantum coherence under strictly incoherent operations (SIO) and physically incoherent operations (PIO), showing that they coincide for all states, and providing a complete description of the phenomenon of bound coherence. In particular, we establish a simple, analytically computable necessary and sufficient criterion for the asymptotic distillability under SIO and PIO. We use this result to show that almost every quantum state is undistillable—only pure states as well as states whose density matrix contains a rank-one submatrix allow for coherence distillation under SIO or PIO, while every other quantum state exhibits bound coherence. This demonstrates the fundamental operational limitations of SIO and PIO in the resource theory of quantum coherence. We show that the fidelity of distillation of a single bit of coherence under SIO can be efficiently computed as a semidefinite program, and investigate the generalization of this result to provide an understanding of asymptotically achievable distillation fidelity.


Lami, L., Regula, B., & Adesso, G. (2019). Generic bound coherence under strictly incoherent operations. Physical Review Letters, 122(15), Article 150402.

Journal Article Type Article
Acceptance Date Mar 20, 2019
Online Publication Date Apr 19, 2019
Publication Date Apr 19, 2019
Deposit Date Apr 29, 2019
Publicly Available Date Apr 29, 2019
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 122
Issue 15
Article Number 150402
Keywords Quantum Physics; Mathematical Physics
Public URL
Publisher URL


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