title: Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence.
abstract: Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. Here, the robustness of coherence is defined and proven to be a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase discrimination task.
authors.affiliation: Dipartimento di Fisica "E. R. Caianiello", Università degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Italy.|School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Carmine
authors.initials: C
authors.lastname: Napoli
authors.affiliation: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Thomas R
authors.initials: TR
authors.lastname: Bromley
authors.affiliation: Dipartimento di Fisica "E. R. Caianiello", Università degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Italy.|School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Marco
authors.initials: M
authors.lastname: Cianciaruso
authors.affiliation: SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom.
authors.forename: Marco
authors.initials: M
authors.lastname: Piani
authors.affiliation: Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick E4L 1E2, Canada.
authors.forename: Nathaniel
authors.initials: N
authors.lastname: Johnston
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