Measuring quantum coherence with entanglement

Streltsov, Alexander; Singh, Uttam; Dhar, Himadri Shekhar; Bera, Manabendra Nath; Adesso, Gerardo

Abstract

Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of coherence as an operational resource are still very limited. Here we show that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. This finding allows us to define a novel general class of measures of coherence for a quantum system of arbitrary dimension, in terms of the maximum bipartite entanglement that can be generated via incoherent operations applied to the system and an incoherent ancilla. The resulting measures are proven to be valid coherence monotones satisfying all the requirements dictated by the resource theory of quantum coherence. We demonstrate the usefulness of our approach by proving that the fidelity-based geometric measure of coherence is a full convex coherence monotone, and deriving a closed formula for it on arbitrary single-qubit states. Our work provides a clear quantitative and operational connection between coherence and entanglement, two landmark manifestations of quantum theory and both key enablers for quantum technologies.

Citation

Streltsov, A., Singh, U., Dhar, H. S., Bera, M. N., & Adesso, G. (2015). Measuring quantum coherence with entanglement. Physical Review Letters, 115(2), Article 020403. https://doi.org/10.1103/PhysRevLett.115.020403

• Journal Article Type: Article
• Acceptance Date: Jun 17, 2015
• Online Publication Date: Jul 8, 2015
• Publication Date: Jul 8, 2015
• Deposit Date: Feb 24, 2017
• Publicly Available Date: Feb 24, 2017
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 115
• Issue: 2
• Article Number: 020403
• DOI: https://doi.org/10.1103/PhysRevLett.115.020403
• Public URL: https://nottingham-repository.worktribe.com/output/757434
• Publisher URL: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.020403