Jing-Ling Chen

Security of quantum key distributions with entangled qudits

We consider a generalization of Ekerts entanglement-based quantum cryptographic protocol where qubits are replaced by N- or d-dimensional systems (qudits). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerfs formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of qudit generalizations of the Ekerts protocol for qubits.

Geometric phases for nondegenerate and degenerate mixed states

This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both nondegenerate as well as degenerate states. Starting with the nondegenerate case, we show that the usual procedure of subtracting the dynamical phase from the total phase to yield the geometric phase for pure states, does not hold for mixed states. To this end, we furnish an expression for the geometric phase that is gauge invariant. The parallelity conditions are shown to be easily derivable from this expression. We also extend our formalism to states that exhibit degeneracies. Here with the holonomy taking on a non-Abelian character, we provide an expression for the geometric phase that is manifestly gauge invariant. As in the case of the nondegenerate case, the form also displays the parallelity conditions clearly. Finally, we furnish explicit examples of the geometric phases for both the nondegenerate as well as degenerate mixed states.

Braiding transformation, entanglement swapping, and Berry phase in entanglement space

We show that braiding transformation is a natural approach to describe quantum entanglement by using the unitary braiding operators to realize entanglement swapping and generate the Greenberger-Horne-Zeilinger states as well as the linear cluster states. A Hamiltonian is constructed from the unitary

Berry phase and quantum criticality in Yang-Baxter systems

{\stackrel{\ifmmode \check{}\else \v{}\fi{}}{R}}_{i,i+1}(\ensuremath{\theta},\ensuremath{\varphi})

Gisin's Theorem for Three Qubits

matrix, where

All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering

\ensuremath{\varphi}=\ensuremath{\omega}t

Entangled three-state systems violate local realism more strongly than qubits: An analytical proof

is time-dependent while

Quantum-dynamical theory for squeezing the output of a Bose-Einstein condensate

\ensuremath{\theta}

Violating Bell inequalities maximally for two d-dimensional systems

is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space.

Higgs algebraic symmetry in the two-dimensional Dirac equation

Abstract Spin interaction Hamiltonians are obtained from the unitary Yang–Baxter R ˘ -matrix. Based on which, we study Berry phase and quantum criticality in the Yang–Baxter systems.