Quantum cryptographic ranging

We present a system to measure the distance between two parties that allows only trusted people to access the result. The security of the protocol is guaranteed by the complementarity principle in quantum mechanics. The protocol can be realized with available technology, at least as a proof of principle experiment.Comment: 2 pages, 1 figure. Contribution to the proceedings of the IV edition of the Garda Lake Workshop "Mysteries, Puzzles and Paradoxes in Quantum Mechanics

The Step-Harmonic Potential

We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit.Comment: 19 pages, 7 figure

Forecasting isocurvature models with CMB lensing information: axion and curvaton scenarios

Some inflationary models predict the existence of isocurvature primordial fluctuations, in addition to the well known adiabatic perturbation. Such mixed models are not yet ruled out by available data sets. In this paper we explore the possibility of obtaining better constraints on the isocurva- ture contribution from future astronomical data. We consider the axion and curvaton inflationary scenarios, and use Planck satellite experimental specifications together with SDSS galaxy survey to forecast for the best parameter error estimation by means of the Fisher information matrix formal- ism. In particular, we consider how CMB lensing information can improve this forecast. We found substantial improvements for all the considered cosmological parameters. In the case of isocurvature amplitude this improvement is strongly model dependent, varying between less than 1% and above 20% around its fiducial value. Furthermore, CMB lensing enables the degeneracy break between the isocurvature amplitude and correlation phase in one of the models. In this sense, CMB lensing information will be crucial in the analysis of future data.Comment: Accepted for publication in PR

Dispersive analysis of the experimental data on the electromagnetic form factor of charged pions at spacelike momenta

The experimental data on the electromagnetic form factor of charged pions available at spacelike momenta are analyzed using the Dispersive Matrix (DM) approach, which describes the momentum dependence of hadronic form factors without introducing any explicit parameterization and includes properly the constraints coming from unitarity and analyticity. The unitary bound is evaluated nonperturbatively making use of the results of lattice QCD simulations of suitable two-point correlation functions contributing to the HVP term of the muon. Thanks to the DM method we determine the pion charge radius from existing spacelike data in a completely model-independent way and consistently with the unitary bound, obtaining $_{DM} = 0.703 \pm 0.027$ fm. This finding differs by $\simeq 1.6$ standard deviations from the latest PDG value $_{PDG} = 0.659 \pm 0.004$ fm, which is dominated by the very precise results of dispersive analyses of timelike data coming from measurements of the cross section of the $e^+ e^- \to \pi^+ \pi^-$ process. We have analyzed the spacelike data using also traditional $z$-expansions, like the Boyd-Grinstein-Lebed (BGL) or Bourrely-Caprini-Lellouch (BCL) fitting functions and adopting a simple procedure that incorporates ab initio the non-perturbative unitary bound in the fitting process. We get $_{BGL} = 0.711 \pm 0.039$ fm and $_{BCL} = 0.709 \pm 0.028$ fm in nice agreement with the DM result. We have addressed also the issue of the onset of perturbative QCD by performing a sensitivity study of the pion form factor at large spacelike momenta, based only on experimental spacelike data and unitarity. Hence, although the leading pQCD behaviour is found to set in only at very large momenta, our DM bands may provide information about the pre-asymptotic effects related to the scale dependence of the pion distribution amplitude.Comment: 39 pages, 21 figures, 4 table

Inter-edge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime

Gate-voltage control of inter-edge tunneling at a split-gate constriction in the fractional quantum Hall regime is reported. Quantitative agreement with the behavior predicted for out-of-equilibrium quasiparticle transport between chiral Luttinger liquids is shown at low temperatures at specific values of the backscattering strength. When the latter is lowered by changing the gate voltage the zero-bias peak of the tunneling conductance evolves into a minimum and a non-linear quasihole-like characteristic emerges. Our analysis emphasizes the role of the local filling factor in the split-gate constriction region.Comment: 4 pages, 4 figure

4e-condensation in a fully frustrated Josephson junction diamond chain

Fully frustrated one-dimensional diamond Josephson chains have been shown [B. Dou\c{c}ot and J. Vidal, Phys. Rev. Lett. {\bf 88}, 227005 (2002)] to posses a remarkable property: The superfluid phase occurs through the condensation of pairs of Cooper pairs. By means of Monte Carlo simulations we analyze quantitatively the Insulator to $4e$-Superfluid transition. We determine the location of the critical point and discuss the behaviour of the phase-phase correlators. For comparison we also present the case of a diamond chain at zero and 1/3 frustration where the standard $2e$-condensation is observed.Comment: 5 pages, 7 figure

Bosonic Memory Channels

We discuss a Bosonic channel model with memory effects. It relies on a multi-mode squeezed (entangled) environment's state. The case of lossy Bosonic channels is analyzed in detail. We show that in the absence of input energy constraints the memory channels are equivalent to their memoryless counterparts. In the case of input energy constraint we provide lower and upper bounds for the memory channel capacity.Comment: 6 pages, 2 figure

Optimal estimation of quantum observables

We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased estimation is achieved by the usual procedure that consists in performing independent measurements of the observable on each system and averaging the measurement outcomes.Comment: Submitted to J. Math Phy

Effect of charging on CdSe/CdS dot-in-rods single-photon emission

The photon statistics of CdSe/CdS dot-in-rods nanocrystals is studied with a method involving post-selection of the photon detection events based on the photoluminescence count rate. We show that flickering between two states needs to be taken into account to interpret the single-photon emission properties. With post-selection we are able to identify two emitting states: the exciton and the charged exciton (trion), characterized by different lifetimes and different second order correlation functions. Measurements of the second order autocorrelation function at zero delay with post- selection shows a degradation of the single photon emission for CdSe/CdS dot-in-rods in a charged state that we explain by deriving the neutral and charged biexciton quantum yields.Comment: 10 pages, 5 figure

Normal form decomposition for Gaussian-to-Gaussian superoperators

In this paper we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix