title: Measuring Quantum Coherence with Entanglement.
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.
authors.affiliation: ICFO-The Institute of Photonic Sciences, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain.
authors.forename: Alexander
authors.initials: A
authors.lastname: Streltsov
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Uttam
authors.initials: U
authors.lastname: Singh
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.|School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.
authors.forename: Himadri Shekhar
authors.initials: HS
authors.lastname: Dhar
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Manabendra Nath
authors.initials: MN
authors.lastname: Bera
authors.affiliation: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Gerardo
authors.initials: G
authors.lastname: Adesso