The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.     

The incompatibility between local hidden variable theories and the fundamental conservation laws

I discuss in detail the result that the Bell’s inequalities derived in the context of local hidden variable theories for discrete quantized observables can be satisfied only if a fundamental conservation law is violated on the average. This result shows that such theories are physically nonviable, and makes the demarcating criteria of the Bell’s inequalities redundant. I show that a unique correlation function can be derived from the validity of the conservation law alone and this coincides with the quantum mechanical correlation function. Thus, any theory with a different correlation function, like any local hidden variable theory, is incompatible with the fundamental conservation laws and space-time symmetries. The results are discussed in the context of two-particle singlet and triplet states, GHZ states, and two-particle double slit interferometry. Some observations on quantum entropy, entanglement, and nonlocality are also discussed.     

The Distance Between Classical and Quantum Systems

In a recent paper, a “distance” function, , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors for simplicity and clarity. Several specific examples are calculated.     

Quantum dynamics of charge transfer on the one-dimensional lattice:Wave packet spreading and recurrence

The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.     

Bidirectional transfer of quantum information for unknown photons via cross-Kerr nonlinearity and photon-number-resolving measurement

We propose an arbitrary controlled-unitary(CU) gate and a bidirectional transfer scheme of quantum information(BTQI) for unknown photons.The proposed CU gate utilizes quantum non-demolition photon-number-resolving measurement based on the weak cross-Kerr nonlinearities(XKNLs) and two quantum bus beams;the proposed CU gate consists of consecutive operations of a controlled-path gate and a gathering-path gate.It is almost deterministic and is feasible with current technology when a strong amplitude of the coherent state and weak XKNLs are employed.Compared with the existing optical multi-qubit or controlled gates,which utilize XKNLs and homodyne detectors,the proposed CU gate can increase experimental realization feasibility and enhance robustness against decoherence.According to the CU gate,we present a BTQI scheme in which the two unknown states of photons between two parties(Alice and Bob) are mutually swapped by transferring only a single photon.Consequently,by using the proposed CU gate,it is possible to experimentally implement the BTQI scheme with a certain probability of success.     

Deformed photon-added entangled squeezed vacuum and one-photon states: Entanglement,polarization, and nonclassical properties

In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variabletype entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f-deformed creation operator A = f(n)aon the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the twomode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f-deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.     

光纤中单光子传输方程的求解及分析

量子信息在光纤中传输时,会受到光纤损耗、色散、非线性效应等多因素的影响,将产生传输态的演化与能量转移.本文以单模光纤传输方程以及电磁场量子化理论为基础,对单模光纤中基模模场进行量子化处理,推导并建立了考虑损耗、色散、非线性效应后的单光子传输方程.基于微扰法对单光子非线性传输方程进行了求解,给出了稳定解存在的必要条件及其所满足的色散方程.深入讨论了广域光功率随微扰频率的变化关系,并且分析了光纤色散、非线性效应对解的影响.为量子光纤传输系统性能的深入研究奠定了理论基础.     

Scanning Tunneling Electron Transport into a Kondo Lattice

We theoretically present the results for a scanning tunneling transport between a metallic tip and a Kondo lattice.We calculate the density of states(DOS)and the tunneling current and differential conductance(DC)under different conduction-fermion band hybridization and temperature in the Kondo lattice.It is found that the hybridization strength and temperature give asymmetric coherent peaks in the DOS separated by the Fermi energy.The corresponding current and DC intensity depend on the temperature and quantum interference effect among the c-electron and f-electron states in the Kondo lattice.     

Constraining Lorentz invariance violation from the continuous spectra of short gamma-ray bursts

In some quantum gravity theories, a foamy structure of space-time may lead to Lorentz invariance violation(LIV). As the most energetic explosions in the Universe, gamma-ray bursts(GRBs) provide an effect way to probe quantum gravity effects. In this paper, we use the continuous spectra of 20 short GRBs detected by the Swift satellite to give a conservative lower limit of quantum gravity energy scale MQG. Due to the LIV effect, photons with different energy have different velocities. This will lead to the delayed arrival of high energy photons relative to low energy ones. Based on the fact that the LIV-induced time delay cannot be longer than the duration of a GRB,we present the most conservative estimate of the quantum gravity energy scales from 20 short GRBs. The strictest constraint, M_(QG) 5.05 × 10~(14) GeV in the linearly corrected case, is from GRB 140622 A. Our constraint on MQG,although not as tight as previous results, is the safest and most reliable so far.