The true role of entanglement in two-photon virtual-state spectroscopy (Saleh et al 1998 Phys. Rev. Lett. 80 3483), a two-photon absorption spectroscopic technique that can retrieve information about the energy level structure of an atom or a molecule, is controversial. The consideration of closely related techniques, such as multidimensional pump-probe spectroscopy (Roslyak et al 2009 Phys. Rev. A 79, 063409), suggests that spectroscopic information might also be retrieved by using uncorrelated pairs of photons. Here we show that this is not the case. In the two-photon absorption process, the ability to obtain information about the energy level structure of a medium depends on the spectral shape of existing temporal (frequency) correlations between the absorbed photons. In fact, it is a combination of both the presence of frequency correlations (entanglement) and their specific spectral shape that makes the

Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a coherent beam, where each spatial mode bears different polarizations. Whereas a local unitary transformation of the system does not affect its coherence, global unitary transformations modifying both the system and its surroundings can enhance its coherence, transforming mutual correlations into coherence. The question naturally arises of what is the best measure that quantifies the correlations that can be turned into coherence, and how much coherence can be extracted. We answer both questions, and illustrate its application for some typical simple systems, with the aim at illuminating the general concept of enhancing coherence by modifying correlations. Introduction.-Coherence is one of the most important concepts needed to describe the characteristics of a stream of photons [1, 2], where it allows us to characterize the interference capability of interacting fields. However its use is far more general as it plays a striking role in a whole range of physical, chemical, and biological phenomena [3]. Measures of coherence can be implemented using classical and quantum ideas, which lead to the question of in which sense quantum coherence might deviate from classical coherence phenomena [4], and to the evaluation of measures of coherence [5][6][7].Commonly used coherence measures consider a physical system as a whole, omitting its structure. The knowledge of the internal distribution of coherence between subsystems and their correlations becomes necessary for predicting the evolution (migration) of coherence in the studied system. The evolution of a twin beam from the near field into the far field represents a typical example occurring in nature [8]. The creation of entangled states by merging the initially separable incoherent and coherent states serves as another example [7]. Or, in quantum computing the controlled-NOT gate entangles (disentangles) two-qubit states [9,10], at the expense (in favor) of coherence. Many quantum metrology and communication applications benefit from correlations of entangled photon pairs originating in spontaneous parametric down-conversion [11][12][13]. Even separable states of photon pairs, i.e. states with suppressed correlations, are very useful, e.g., in the heralded single photon sources [14,15]. For all of these, and many others, examples the understanding of common evolution of coherence and correlations is crucial.The Clauser-Horne-Shimony-Holt (CHSH) Bell's-like inequality [16][17][18] has been usually considered to quantify nonclassical correlations present between physically sepa-

Entangled two-photon absorption spectroscopy (TPA) has been widely recognized as a powerful tool for revealing relevant information about the structure of complex molecular systems. However, to date, the experimental implementation of this technique has remained elusive, mainly because of two major difficulties. First, the need to perform multiple experiments with two-photon states bearing different temporal correlations, which translates into the necessity to have at the experimenter's disposal tens, if not hundreds, of sources of entangled photons. Second, the need to have a priori knowledge of the absorbing medium's lowest-lying intermediate energy level. In this work, we put forward a simple experimental scheme that successfully overcomes these two limitations. By making use of a temperature-controlled entangled-photon source, which allows the tuning of the central frequencies of the absorbed photons, we show that the TPA signal, measured as a function of the temperature of the nonlinear crystal that generates the paired photons, and a controllable delay between them, carries all information about the electronic level structure of the absorbing medium, which can be revealed by a simple Fourier transformation.