Generic bound coherence under strictly incoherent operations

Lami, Ludovico; Regula, Bartosz; Adesso, Gerardo

Abstract

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.

Citation

Lami, L., Regula, B., & Adesso, G. (2019). Generic bound coherence under strictly incoherent operations. Physical Review Letters, 122(15), Article 150402. https://doi.org/10.1103/physrevlett.122.150402

• 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
• DOI: https://doi.org/10.1103/physrevlett.122.150402
• Keywords: Quantum Physics; Mathematical Physics
• Public URL: https://nottingham-repository.worktribe.com/output/1849809
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.150402
• Contract Date: Apr 29, 2019