Multipliers on a new class of Banach algebras, locally compact quantum groups, and topological centres

We study multiplier algebras for a large class of Banach algebras which contains the group algebra $L_1(G)$, the Beurling algebras $L_1(G, \omega)$, and the Fourier algebra $A(G)$ of a locally compact group $G$. This study yields numerous new results and unifies some existing theorems on $L_1(G)$ and $A(G)$ through an abstract Banach algebraic approach. Applications are obtained on representations of multipliers over locally compact quantum groups and on topological centre problems. In particular, five open problems in abstract harmonic analysis are solved.Comment: 38 page

Protecting Two-Qubit Quantum States by π\pi-Phase Pulses

We study the state decay of two qubits interacted with a common harmonic oscillator reservoir. There are both decoherence error and the error caused by the amplitude change of the superradiant state. We show that frequent $\pi$-phase pulses can eliminate both typpes of errors therefore protect a two-qubit odd-parity state more effectively than the frequent measurement method. This shows that the the methods using dynamical decoupling and the quantum Zeno effects actually can give rather {\em different} results when the operation frequency is finite