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Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehaviour of this operator occurs whenever the operator's weak value exceeds its eigenvalue bound. We give illustrative examples of this effect for total angular momentum and energy. In the later case, we demonstrate a sequence of harmonic oscillator potentials where a finite energy state converges everywhere on the real line, using only bounded superpositions of states whose asymptotic energy vanishes - "energy out of nothing". We resolve this paradoxical situation by showing the time-dependent Schr\"odinger equation no longer applies in the considered limit because of the non-commutation of the limit with the time-derivative. Nevertheless, this example demonstrates the possibility of mimicking a high-energy state with coherent superpositions of nearly zero-energy states for as wide a spatial region as desired., Comment: 6 pages, 4 figures

We show how weak non-linearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schr��dinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that over any distance in this channel the quantum bit error rate is identically zero, in principle, and the states in the protocol are always able to violate a Bell inequality. The protocol is found to be superior in some regimes to a device-independent QKD protocol based on polarization entangled states in a depolarizing channel. Finally, we propose an implementation for the optimal filters and measurements., Comments welcome

We show how one can demonstrate continuous-variable Einstein-Podolsky-Rosen (EPR) steering without needing to characterize entire measurement probability distributions. To do this, we develop a modified Fano inequality useful for discrete measurements of continuous variables, and use it to bound the conditional uncertainties in continuous-variable entropic EPR-steering inequalities. With these bounds, we show how one can hedge against experimental limitations including a finite detector size, dead space between pixels, and any such factors that impose an incomplete sampling of the true measurement probability distribution. Furthermore, we use experimental data from the position and momentum statistics of entangled photon pairs in parametric downconversion to show that this method is sufficiently sensitive for practical use., 7 pages, 2 figures

We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom., 10 pages, 2 figures

We implement a double-pixel, compressive sensing camera to efficiently characterize, at high resolution, the spatially entangled fields produced by spontaneous parametric downconversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster-scanning by a scaling factor up to n^2/log(n) for n-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates compressive sensing can be especially effective for higher-order measurements on correlated systems., 10 pages, 7 figures

We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a novel experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost imaging central image plane, we are able to dramatically increase the ghost image quality. When imaging a test pattern through turbulence, this method increased the imaged pattern visibility from V = 0.14 +/- 0.04 to V = 0.29 +/- 0.04.

This article has been withdrawn.

Inspired by laser operation, we address the question of whether stimulated emission into polarization entangled modes can be achieved. We describe a state produced by stimulated emission of the singlet Bell state and propose a setup for creating it. As a first important step towards an entangled-photon laser we demonstrate experimentally interference-enhanced polarization entanglement., Comment: 8 pages, 3 figures, revtex 4, submitted to PRL November 2000