Polar codes and polar lattices for the Heegard-Berger problem

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for doublysymmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting a quantization polar lattice and a capacity-achieving polar lattice for the additive white Gaussian noise channel

Trapped ion quantum computation with transverse phonon modes

We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.Comment: 5 page

Spin Hall effects for cold atoms in a light induced gauge potential

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.Comment: 4 pages; The published versio

A simple encoding of a quantum circuit amplitude as a matrix permanent

A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This opens up some interesting classical monte-carlo algorithms for approximating quantum circuits.Comment: 6 figure

Polarizabilities of the 87Sr Clock Transition

In this paper, we propose an in-depth review of the vector and tensor polarizabilities of the two energy levels of the 87Sr clock transition whose measurement was reported in [P. G. Westergaard et al., Phys. Rev. Lett. 106, 210801 (2011)]. We conduct a theoretical calculation that reproduces the measured coefficients. In addition, we detail the experimental conditions used for their measurement in two Sr optical lattice clocks, and exhibit the quadratic behaviour of the vector and tensor shifts with the depth of the trapping potential and evaluate their impact on the accuracy of the clock