In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind of quantum correlation which we call correlated coherence. We demonstrate that the framework provided by correlated coherence allows us to retrieve the same concepts of quantum correlations as defined by the asymmetric and symmetric versions of quantum discord as well as quantum entanglement, providing a unified view of these correlations. We also prove that correlated coherence can be formulated as an entanglement monotone, thus demonstrating that entanglement may be viewed as a specialized form of coherence.

In this Letter, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present in an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource theory introduced by Baumgratz, Cramer, and Plenio and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan $P$ distribution. This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum light. We show that our construction belongs to a family of resource monotones within the framework of a resource theory of linear optics, thus establishing deeper connections between the class of incoherent operations in the finite dimensional regime and linear optical operations in the continuous variable regime.

In this review, the authors introduce the notion of quantum nonclassicality of light and the role of nonclassicality in optical quantum metrology. The first part of this paper focuses on defining and characterizing the notion of nonclassicality and how it may be quantified in radiation fields. Several prominent examples of nonclassical light are also discussed. The second part of this paper deals with quantum metrology through the lens of nonclassicality. The authors introduce key concepts such as the Quantum Fisher information, the Cramér-Rao bound, the standard quantum limit, and the Heisenberg limit and discuss how nonclassical light may be exploited to beat classical limitations in high precision measurements. The discussion here will be largely theoretical, with some references to specific experimental implementations.

We demonstrate that the negative volume of any $s$-parametrized quasiprobability, including the Glauber-Sudashan $P$ function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical monotones. These measures belong to an operational resource theory of nonclassicality based on linear optical operations. The negativity of the Glauber-Sudashan $P$ function, in particular, can be shown to have an operational interpretation as the robustness of nonclassicality. We then introduce an approximate linear optical monotone, and we show that this nonclassicality quantifier is computable and is able to identify the nonclassicality of nearly all nonclassical states.

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation of unitarily encoded parameters. Finally, we extend the results to show that the Fisher information is also able to identify the dynamical resourcefulness of quantum operations.

We demonstrate that quantum Fisher information and superradiance can be formulated as coherence measures in accordance with the resource theory of coherence, thus establishing a direct link between metrological resources, superradiance, and coherence. The arguments are generalized to show that coherence may be considered as the underlying fundamental resource for any functional of state that is first of all faithful, and second, concave or linear. It is also shown that quantum Fisher information and the superradiant quantity are in fact antithetical resources in the sense that if coherence were directed to saturate one quantity, then it must come at the expense of the other. Finally, a key result of the paper is to demonstrate that coherence, quantum Fisher information, superradiant quantity, and entanglement are mutually interconvertible resources under incoherent operations.