Quantum Correlation Coefficients for Angular Coherent States

Quantum covariance and correlation coefficients of angular or SU（2） coherent states are directly calculated for all irreducible unitary representations. These results explicitly verify that the angular coherent states minimize the Robertson-Schrodinger uncertainty relation for all spins, which means that they are the so-called intelligent states. The same results can be obtained by the Schwinger representation approach.     

Sudden birth and sudden death of thermal fidelity in a two-qubit system

We study the energy level crossing and the thermal fidelity in a two-qubit system with the presence of a transverse inhomogeneous magnetic field.With the help of contour plots,we clearly identify the ground states of the system in different regions of parameter space,and discuss the corresponding energy level crossing.The fidelity between the ground state of the system and the state of the system at temperature T is calculated.The result shows that the fidelity is very sensitive to the magnetic field anisotropic factor,indicating that this factor may be used as a controller of the fidelity.The influence of the Yangian transition operators on the fidelity of the system is discussed.We find that the Yangian operators can change the fidelity dramatically and give rise to sudden birth and sudden death phenomena of the thermal fidelity.This makes the corresponding Yangian operators possible candidates for switchers to turn the fidelity on and off.     

Chaotic behaviours and control of chaos in the p-Ge photoconductor

The chaotic behaviours in the p--Ge photoconductor system are studied by changing the photo-excitation coefficient and the routes and parameter conditions are given for chaos generation in this system. A scheme for controlling chaos in the p--Ge photoconductor is presented by adding an ac bias current. Numerical simulations show that this scheme can be effectively used to control chaotic states into stable period states for this system. Moreover, the different period states with different period numbers can be obtained by appropriately adjusting the amplitude, frequency, and initial phase of the additional ac current.     

Active manipulation of the selective alignment by two laser pulses

This paper solves numerically the full time-dependent Schrdinger equation based on the rigid rotor model, and proposes a novel strategy to determine the optimal time delay of the two laser pulses to manipulate the molecular selective alignment. The results illustrate that the molecular alignment generated by the first pulse can be suppressed or enhanced selectively, the relative populations of even and odd rotational states in the final rotational wave packet can be manipulated selectively by precisely inserting the peak of the second laser pulse at the time when the slope for the alignment parameter by the first laser locates a local maximum for the even rotational states and a local minimum for the odds, and vice versa. The selective alignment can be further optimised by selecting the intensity ratio of the two laser pulses on the condition that the total laser intensity and pulse duration are kept constant.     

Remote interactions on two distributed quantum systems： nonlocal unambiguous quantum-state discrimination

Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement （POVM）. We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM.     

Brownian dynamics simulation of the cross-talking effect among modified histones on conformations of nucleosomes

Using Brownian dynamics simulation,we studied the effect of histone modifications on conformations of an array of nucleosomes in a segment of chromatin.The simulation demonstrated that the segment of chromatin shows the dynamic behaviour that its conformation can switch between a state with nearly all of the histones being wrapped by DNA and a state with nearly all of the histones being unwrapped by DNA,thus involving the "cross-talking" interactions among the histones.Each state can stay for a sufficiently long time.These conformational states are essential for gene expression or gene silence.The simulation also shows that these conformational states can be inherited by the daughter DNAs during DNA replication,giving a theoretical explanation of the epigenetic phenomenon.     

One-to-Many Economical Phase-Covariant Cloning and Telecloning of Qudits

We present explicit unitary transformations for realizing both symmetric and asymmetric one-to-many economical phase-covariant clonings of qudits. We also propose a corresponding telecloning scheme. It is shown that the fidelity of the telecloning with nonmaximally entangled states can be larger than that of the corresponding cloning. This implies that partially entangled states can be better than the maximally entangled states for our economical phase-covariant telecloning scheme.     

Quantum Generalized Subspace Projector Measurement and Measurement Induced Entanglement

We propose the concept of the quantum generalized subspace projector measurement （QGSPM）. The distinguished properties of QGSPM is revealed： no matter what the state of the system is prior to the measurement and what the measured result occurs, the state posterior to the measurement can be collapsed onto the specified subspace. Subsequently, the quantum generalized case-projector measurement （QGCPM）, as a special case of QGSPM, is also discussed carefully. It is demonstrated that no matter what measured result occurs, the state of the system posterior to QGCPM can be collapsed into one of pure states. Consequently, QGCPM can be used to generate the maximally entangled pure states for multiple particles. As illustrative examples, several concrete methods of generating entanglement are proposed for two two-level particles. It is found that the maximally entangled pure states of two 2-level particles can be generated just by a single QGCPM and the corresponding QGCPM operators are physically realizable in principle if an ancillary four-dimensional quantum system can be introduced.     

Improving the fidelity of continuous-variable quantum teleportation by tuning displacement gain

The fidelity of teleportation of continuous quantum variables can be improved by tuning the local displacement gain. We investigate the optimization of the fidelity for the teleportation of Schrodinger cat states, and of coherent states. It is found that the gain corresponding to the maximum fidelity is not equal to one for the two input states in the case of the small squeezing degree of the entanglement resource, while unity displacement gain is the best choice for teleporting arbitrary quantum states in the case of large squeezing.     

Anti-control of chaos in p--Ge photoconductor

We present a scheme for the anti-control of chaos in the p--Ge photoconductor system by using a chaotic laser to irradiate and disturb this system. The numerical simulations show that this scheme can be effectively used to control periodic states in this p--Ge system into chaotic states. Moreover, the different chaos states with different chaotic orbits can be obtained by appropriately adjusting the disturbance intensity and disturbance frequency, and by increasing this intensity or reducing this frequency, this p--Ge system gradually evolves to fully developed chaotic states.     

Yangians and transition operators

Yangian has emerged as a underlying algebraic structure for quantum spin chains with inverse-square exchange interactions. Recently, it has also been found that the Yangian can be regarded as an extended dipole operator or transition operator connecting different highest weight states. In this report, we describe how Yangian can be used to construct the shift operators associated with the spin chain. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. This work was supported by NUS Research Grant No. RP3982713.     

Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

Application of Y（sl（2）） Algebra for Entanglement of Two-Qubit System

We construct the transition operators in terms of the generators of the general Yangian and the reduced Yangian. By acting these operators on a two-qubit pure state, we find that the entanglement degrees of the states are all decreased from the certain values to zero for the reduced Yangian algebra, which makes the state disentangled. This result sheds new light on the physical meaning of Y （sl（2） ） in quantum information.     

Yangian代数在混合介子态的纠缠和衰变中的应用

Yangian代数是超出李代数更大的无穷维代数,是研究非线性量子完全可积系统的新对称特性的有力数学工具.基于介子态中夸克-味su(3)对称性和Yangian代数生成元的跃迁特性,本文研究了Yangian代数Y(su(3))生成元在三种正反介子态(π~±,K~±,K~0和K~0)各自组成的三种混合介子态(π,K和K_i~0)衰变中的作用.将Y(su(3))代数的八个生成元(I~±,U~±,V~±,I~3和I~8)作为跃迁算子,作用在混合介子态上,研究其可能的衰变道,以及衰变前后纠缠度的变化.结果表明:1)在李代数范围内的生成元I~3和I~8作用下,三种混合介子态衰变后组成成分没有发生变化,其中混合介子态π在I~8作用下衰变前后纠缠无变化,其他衰变纠缠度发生了变化;2)在其他的六个(I~±,U~±和V~±)超出李代数的生成元的作用下,三种混合介子态衰变前后组成成分发生了变化,其中两个衰变后变成单态,纠缠度为零;两个衰变不存在;剩余两个衰变后纠缠度发生了变化,此外在带电(K)和中性(K_I~0)两类K型混合介子态的六种可能的衰变中,两种类型的末态的纠缠度两两相同;3)三种混合介子态之间可以通过I~±,U~±和V~±算子循环转化,具有明显的对称性.本文从具有的对称性上提供了一种探索混合介子态可能衰变的方法,并且可以用此方法去预测可能的未知衰变粒子和解释己测得的衰变问题.     

h-Miura Transformation in the DYh(sl2)k Case

The h-analogue of the Sugawara operater is constructed for the Yangian double with central extension in the sl₂ case.Using the free fields realization of the quantum currents,the h-analogue Miura transformation is obtained.     

Spin models and superconformal Yang–Mills theory

We apply novel techniques in planar superconformal Yang–Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local Abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability.     

A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field

Yangian Y(sl(2)) is realized in the bi-spin system coupled with a time-dependent external magnetic field. It is shown that Y(sl(2)) generators can describe the transitions between the "spin triplet" and the "spin singlet" that evolve with time. Furthermore, new transition operators between the states with Berry phase factor and those between the states of nuclear magnetic resonance are presented.     

Symmetries and exact solutions of some integrable Haldane-Shastry-like spin chains

Here we construct some integrable Haldane-Shastry (HS) like spin chains, which exhibit multi-parameter deformed or non-standard variants of Y(gl_m) Yangian symmetry. By projecting the eigenstates of Dunkl operators in a suitable way, we also derive a class of exact eigenfunctions for such spin chains and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states (HWS) associated with multi-parameter deformed or non-standard variants of Y(gl_M) Yangian algebra. By using this conjecture, and acting descendent operator on the HWS associated with a non-standard Y(gl₂) Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS-like chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of the above mentioned HS-like spin chain with non-standard Y(gl²) symmetry.     

Parabolic Presentations of the Super Yangian Y(\mathfrakglM|N){Y(\mathfrak{gl}_{M|N})}

Associated to a composition of M and a composition of N, a new presentation of the super Yangian of the general linear Lie superalgebra Y(\mathfrakgl_M|N){Y(\mathfrak{gl}_{M|N})} is obtained.