Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing

In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented

Risk- & Regret-Averse Bidders in Sealed-Bid Auctions

Overbidding, bidding more than risk-neutral Bayesian Nash Equilibrium, is a widely observed phenomenon in virtually all experimental auctions. The scholars within the auction literature propose the risk-averse preference model to explain overbidding structurally. However, the risk-averse preference model predicts underbidding in such important classes of auctions as all-pay auctions. To solve this discrepancy, we construct a structural model of bidding behavior in sealed-bid auctions, one in which bidders may regret their decisions. Our model nests both risk-averse and regret-averse attitudes and aims to explain overbidding in a wider class of auctions. We first derive equilibrium first-order conditions, which are used for estimation and calibration analyses, and show monotonic increasing properties of equilibrium bidding functions. Second, we carry out structural estimation and calibration analyses based on experimental data from Kagel and Levin (1993) and Noussair and Silver (2006). With these structurally estimated parameters, we test the significance of bidders’ risk-averse and regret-averse attitudes. The estimation results show that bidders exhibit weak risk-averse (close to risk-neutral) and strong regret-averse attitudes. Furthermore, regret-averse attitudes are significant when bidders anticipate losing. Calibration results demonstrate that our risk- & regret-averse model can explain overbidding across all of the above IPV auctions. Third, we simulate our model with the estimated parameters and obtain revenue rankings numerically. This allows us to confirm the revenue supremacy in all-pay auctions reported in experimental auction literature. We discuss extensions to asymmetric and Common-Value (CV) auctions in our online appendix

Nonlinear cancellation of the parametric resonance in elastic beams: theory and experiment

A non-linear control strategy is applied to a simply supported uniform elastic beam subjected to an axial end force at the principal-parametric resonance frequency of the first skew-symmetric mode. The control input consists of the bending couples applied by two pairs of piezoceramic actuators attached onto both sides of the beam surfaces and symmetrically with respect to the midspan, driven by the same voltage, thus resulting into symmetric control forces. This control architecture has zero control authority, in a linear sense, onto skew-symmetric vibrations. The non-linear transfer of energy from symmetric motions to skew-symmetric modes, due to non-linear inertia and curvature effects, provides the key physical mechanism for channelling suitable control power from the actuators into the linearly uncontrollable mode. The reduced dynamics of the system, constructed with the method of multiple scales directly applied to the governing PDE’s and boundary conditions, suggest effective forms of the control law as a two-frequency input in sub-combination resonance with the parametrically driven mode. The performances of different control laws are investigated. The relative phase and frequency relationships are designed so as to render the control action the most effective. The control schemes generate non-linear controller forces which increase the threshold for the activation of the parametric resonance thus resulting into its annihilation. The theoretical predictions are compared with experimentally obtained results

Universal entanglement concentration

We propose a new protocol of \textit{universal} entanglement concentration, which converts many copies of an \textit{unknown} pure state to an \textit{% exact} maximally entangled state. The yield of the protocol, which is outputted as a classical information, is probabilistic, and achives the entropy rate with high probability, just as non-universal entanglement concentration protocols do. Our protocol is optimal among all similar protocols in terms of wide varieties of measures either up to higher orders or non-asymptotically, depending on the choice of the measure. The key of the proof of optimality is the following fact, which is a consequence of the symmetry-based construction of the protocol: For any invariant measures, optimal protocols are found out in modifications of the protocol only in its classical output, or the claim on the product. We also observe that the classical part of the output of the protocol gives a natural estimate of the entropy of entanglement, and prove that that estimate achieves the better asymptotic performance than any other (potentially global) measurements.Comment: Revised a lot, especially proofs, though no change in theorems, lemmas itself. Very long, but essential part is from Sec.I to Sec IV-C. Some of the appendces are almost independent of the main bod

CIRCULAR DICHROISM OF LIGHT-HARVESTING COMPLEXES FROM PURPLE PHOTOSYNTHETIC BACTERIA

The CD spectra of a range of antenna complexes from several different species of purple photosynthetic bacteria were recorded in the wavelength range of 190 to 930 nm. Analysis of the far UV CD (190 to 250 nm) showed that in each case except for the B800-850 from Chr. vinosum the secondary structure of the light-harvesting complexes contains a large amount of α-helix (50%) and very little 0-pleated sheet. This confirms the predictions of the group of Zuber of a high a-helical content based upon consideration of the primary structures of several antenna apoproteins. The CD spectra from the carotenoids and the bacteriochlorophylls show considerable variations depending upon the type of antenna complex. The different amplitude ratios in the CD spectrum for the bacteriochlorophyll Qy, Qx and Soret bands indicate not only different degrees of exciton coupling, but also a strong and variable hyperchromism (Scherz and Parson, 1984a, b)

Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation

We discuss two quantum analogues of Fisher information, symmetric logarithmic derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher information from a large deviation viewpoint of quantum estimation and prove that the former gives the true bound and the latter gives the bound of consistent superefficient estimators. In another comparison, it is shown that the difference between them is characterized by the change of the order of limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st

Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $\Theta$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the Boltzmann constant), except in the linear response regime, where the fluctuation dissipation theorem holds. In order to elucidate the physical meaning of $\Theta$ far from equilibrium, we analyze a modulated system with a slowly varying potential. We derive a large scale description of the probability density for the modulated system by use of a perturbation method. The expressions we obtain show that $\Theta$ plays the role of the temperature in the large scale description of the system and that $\Theta$ can be determined directly in experiments, without measurements of the diffusion constant and the differential mobility

Asymptotic estimation theory for a finite dimensional pure state model

The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample.Comment: LaTeX, 23 pages, Doctoral Thesi