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.

We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.

Abstract:We demonstrate experimentally that spontaneous parametric down-conversion in an Al x Ga 1−x As semiconductor Bragg reflection waveguide can make for paired photons highly entangled in the polarization degree of freedom at the telecommunication wavelength of 1550 nm. The pairs of photons show visibility higher than 90% in several polarization bases and violate a Clauser-Horne-Shimony-Holt Bell-like inequality by more than 3 standard deviations. This represents a significant step toward the realization of efficient and versatile self pumped sources of entangled photon pairs on-chip.

We put forward a versatile and highly scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small number of simple optical components arranged in a multipath Mach-Zehnder-like configuration, where a weak coherent state is injected. Environmental effects (decoherence) are generated by a spatial light modulator, which introduces pure dephasing in the transverse spatial plane perpendicular to the direction of propagation of the light beam. By controlling the characteristics of this dephasing, one can explore a great variety of scenarios of quantum random walks: pure quantum evolution (ballistic spread), fast fluctuating environment leading to a diffusive classical random walk, and static disorder resulting in the observation of Anderson localization.

In this contribution we analyze virtual-state spectroscopy -a unique tool for extracting information about the virtual states that contribute to the two-photon excitation of an absorbing medium -as implemented by means of intense entangled beams with tunable spectral correlations. We provide a thorough description of all contributing terms (classical and quantum) in the two-photon absorption signal, as well as the limits imposed by the power of the pump that produces the entangled beams on the observability of the spectral lines of the virtual transitions. We find that virtual-state spectroscopy may be implemented with entangled twin beams carrying up to 10 4 photon pairs. This implies that, in principle, one might be able to detect two-photon absorption signals up to four orders of magnitude larger than previously reported, thus paving the way towards the first experimental realization of the virtual-state spectroscopy technique.

Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness producing seemingly contra-intuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well expected outcomes of the experiment. In quantum mechanics (QM) particles are assigned a wave function used to describe their properties [1]. This approach sometimes leads to conclusions about experimental results that seem to contradict intuitive estimations based on classical physics [2,3]. Despite this flaw, QM is currently widely accepted as a theory [1,4], that makes accurate predictions in agreement with the performed experiments. Therefore, it is considered valid regularly used for the interpretation of the results of the corresponding experiments.Recently, an experiment that contained counterintuitive features was proposed and realized by Danan et al. [5]. The authors used nested Mach-Zehnder interferometers (MZI), shown in Fig. 1, and mirrors (A, B, C, E, F) vibrating with different frequencies, in order to leave a mark on passing photons. At one selected output port of the interferometer, the photons were detected by a quad-cell detector D capable of tracing the spatial vibrations of the photon beam. After measurement, the collected signal was further processed and subjected to the Fourier transform. From the obtained frequencies of vibrations, the authors judged whether the detected photons have interacted with the mirror that was oscillating at this particular frequency.The results described in the article by Danan et al. ence inside the interferometer, the correct application of TSVF, the processing of the obtained data and its validity. Until now, no-one has managed to provide the theoretical calculations and the interpretation of the experimental results using only the standard one-state vec-