Shao-Ming Fei

A note on invariants and entanglements

Quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for N-dimensional quantum systems is presented. This generalized concurrence has potential applications in studying separability and calculating the entanglement of formation for high-dimensional mixed quantum states.

Teleportation of general finite-dimensional quantum systems

Abstract Teleportation of finite-dimensional quantum states by a nonlocal entangled state is studied. For a generally given entangled state, an explicit equation that governs the teleportation is presented. Detailed examples and the roles played by the dimensions of the Hilbert spaces related to the sender, receiver and the auxiliary space are discussed.

A remark on symmetry of stochastic dynamical systems and their conserved quantities

The symmetry properties of stochastic dynamical systems described by a stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given by applying symmetry operators to known conserved quantities. Some detailed examples are presented.

An exactly solvable model of generalized spin ladder

A detailed study of an S = ½ spin ladder model is given. The ladder consists of plaquettes formed by nearest-neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown to be integrable in the sense that the quantum Yang-Baxter equation holds and one has an infinite number of conserved quantities. The R-matrix and L-operator associated with the model Hamiltonian are given in a limiting case. It is shown that after a simple transformation, the model can be solved via a Bethe ansatz. The phase diagram of the ground state is exactly derived using the Bethe ansatz equation.

Some new exact ground states for generalized Hubbard models

A set of new exact ground states of the generalized Hubbard models in arbitrary dimensions with explicitly given parameter regions is presented. This is based on a simple method for constructing exact ground states for homogeneous quantum systems.

A remark on the optimal cloning of an N-level quantum system

Abstract:We study quantum cloning machines (QCM) that act on an unknown N-level quantum state and make M copies. We give a formula for the maximum of the fidelity of cloning and exhibit the unitary transformations that realize this optimal fidelity. We also extend the results to treat the case of M copies from identical N-level quantum systems.

Many body problems with "spin"-related contact interactions

Abstract We study quantum mechanical systems with “spin”-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.

Integrable Poisson algebras and two-dimensional manifolds

The relations between integrable Poisson algebras with three generators and two-dimensional symplectic manifolds are investigated. It is shown that for a given integrable Poisson algebra there exists a two-dimensional symplectic manifold such that the Poisson algebra generated by the coordinates of M coincides with the algebra . Vice versa the coordinates of a given smooth two-dimensional symplectic manifold M embedded in generate an integrable Poisson algebra. Moreover, smooth Poisson algebraic maps between two integrable Poisson algebras are governed by equations involving the symplectic manifolds corresponding to these algebras.

Highest weight representations of quantum current algebras

We study the highest weight and continuous tensor product representations ofq-deformed Lie algebras through the mappings of a manifold into a locally compact group. As an example the highest weight representation of theq-deformed algebra slq(2,ℂ) is calculated in detail.

Integrable stochastic ladder models

A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to a series of integrable systems. It is shown that corresponding to these SU(2) symmetric integrable ladder models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov processes with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.