Bosonization of quantum sine-Gordon field with a boundary

Boundary operators and boundary ground states in sine-Gordon model with a fixed boundary condition are studied using bosonization and q-deformed oscillators.We also obtain the form-factors of this model.Comment: Latex 25page

Distributed entanglement induced by dissipative bosonic media

We describe a scheme with analytic result that allows to generate steady-state entanglement for two atoms over a dissipative bosonic medium. The resonant coupling between the mediating bosonic mode and cavity modes produces three collective atomic decay channels. This dissipative dynamics, together with the unitary process induced by classical microwave fields, drives the two atoms to the symmetric or asymmetric entangled steady state conditional upon the choice of the phases of the microwave fields. The effects on the steady-state entanglement of off-resonance mediating bosonic modes are analyzed. The entanglement can be obtained with high fidelity regardless of the initial state and there is a linear relation in the scaling of the fidelity with the cooperativity parameter. The fidelity is insensitive to the fluctuation of the Rabi frequencies of the classical driving fields.Comment: to appear in Europhysics Letter

Reward Teaching for Federated Multi-armed Bandits

Most of the existing federated multi-armed bandits (FMAB) designs are based on the presumption that clients will implement the specified design to collaborate with the server. In reality, however, it may not be possible to modify the clients' existing protocols. To address this challenge, this work focuses on clients who always maximize their individual cumulative rewards, and introduces a novel idea of ``reward teaching'', where the server guides the clients towards global optimality through implicit local reward adjustments. Under this framework, the server faces two tightly coupled tasks of bandit learning and target teaching, whose combination is non-trivial and challenging. A phased approach, called Teaching-After-Learning (TAL), is first designed to encourage and discourage clients' explorations separately. General performance analyses of TAL are established when the clients' strategies satisfy certain mild requirements. With novel technical approaches developed to analyze the warm-start behaviors of bandit algorithms, particularized guarantees of TAL with clients running UCB or epsilon-greedy strategies are then obtained. These results demonstrate that TAL achieves logarithmic regrets while only incurring logarithmic adjustment costs, which is order-optimal w.r.t. a natural lower bound. As a further extension, the Teaching-While-Learning (TWL) algorithm is developed with the idea of successive arm elimination to break the non-adaptive phase separation in TAL. Rigorous analyses demonstrate that when facing clients with UCB1, TWL outperforms TAL in terms of the dependencies on sub-optimality gaps thanks to its adaptive design. Experimental results demonstrate the effectiveness and generality of the proposed algorithms.Comment: Accepted to IEEE Transactions on Signal Processin