Fabricio Toscano

Entropic Entanglement Criteria for Continuous Variables

We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known variance product tests in the case of Gaussian states. Furthermore, they involve only a pair of quadrature measurements, and will thus prove extremely useful in the experimental identification of entanglement.

Sub-Planck phase-space structures and Heisenberg-limited measurements

We show how sub-Planck phase-space structures in the Wigner function [W. H. Zurek, Nature (London) 412, 712 (2001)] can be used to achieve Heisenberg-limited sensitivity in weak-force measurements. Nonclassical states of harmonic oscillators, consisting of superpositions of coherent states, are shown to be useful for the measurement of weak forces that cause translations or rotations in phase space, which is done by entangling the quantum oscillator with a two-level system. Implementations of this strategy in cavity QED and ion traps are described.

Propagation of transverse intensity correlations of a two-photon state

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly correlated photon pairs in an Einstein-Podolsky-Rosen-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anticorrelation, or no correlation, depending on the sum of the orders

Detection of transverse entanglement in phase space

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How do wave packets spread? Time evolution on Ehrenfest time scales

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Observation of tunable Popescu-Rohrlich correlations through postselection of a Gaussian state

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Optimal uncertainty relations for extremely coarse-grained measurements

of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between the theory and experiment.

Quantum entanglement beyond Gaussian criteria

Transverse entanglement between pairs of photons can be detected through intensity correlation measurements in the near and far fields. We show theoretically and experimentally that at intermediate zones, it is also possible to detect transverse entanglement performing only intensity correlation measurements. Our results are applicable to a number of physical systems.

Experimental observation of quantum chaos in a beam of light

We derive an extension of the standard time-dependent WKB theory, which can be applied to propagate coherent states and other strongly localized states for long times. It in particular allows us to give a uniform description of the transformation from a localized coherent state to a delocalized Lagrangian state, which takes place at the Ehrenfest time. The main new ingredient is a metaplectic operator that is used to modify the initial state in a way that the standard time-dependent WKB theory can then be applied for the propagation. We give a detailed analysis of the phase space geometry underlying this construction and use this to determine the range of validity of the new method. Several examples are used to illustrate and test the scheme and two applications are discussed. (i) For scattering of a wave packet on a barrier near the critical energy, we can derive uniform approximations for the transition from reflection to transmission. (ii) A wave packet propagated along a hyperbolic trajectory becomes a Lagrangian state associated with the unstable manifold at the Ehrenfest time; this is illustrated with the kicked harmonic oscillator.

Phase space structure of generalized Gaussian cat states

We show that nonlocal Popescu-Rohrlich correlations can be observed in the postselected results of binned position measurements on a two-party Gaussian state. Our experiment is based on the spatial correlations of entangled photons and lens systems. We obtain a maximum violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality of 3.42, which corresponds to the implementation of a nonlocal AND gate with success probability of 0.93. These results do not conflict with quantum mechanics due to the postselection required and open up the possibility of experimental investigation of fundamental aspects of Popescu-Rohrlich nonlocality with a reliable and simple experimental setup.