We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in p...We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.展开更多
Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaus...Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations（namely subtracting and adding a single photon）, we propose a scheme to generate non-Gaussian quantum states named single-photon-added and-subtracted coherent（SPASC） superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of nonGaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states（DCSS）. The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10674162 and 10575080, and the National Basic Research Programme of China under Grant No 2006CB921107.
文摘We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.
基金supported by the National Natural Science Foundation of China(Grant Nos.61203061 and 61074052)the Outstanding Young Talent Foundation of Anhui Province,China(Grant No.2012SQRL040)the Natural Science Foundation of Anhui Province,China(Grant No.KJ2012Z035)
文摘Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations（namely subtracting and adding a single photon）, we propose a scheme to generate non-Gaussian quantum states named single-photon-added and-subtracted coherent（SPASC） superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of nonGaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states（DCSS）. The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively.
