A Systems Theory Approach to the Synthesis of Minimum Noise Phase-Insensitive Quantum Amplifiers

We present a systems theory approach to the proof of a result bounding the required level of added quantum noise in a phase-insensitive quantum amplifier. We also present a synthesis procedure for constructing a quantum optical phase-insensitive quantum amplifier which adds the minimum level of quantum noise and achieves a required gain and bandwidth. This synthesis procedure is based on a singularly perturbed quantum system and leads to an amplifier involving two squeezers and two beamsplitters.Comment: To appear in the Proceedings of the 2018 European Control Conferenc

Cohomology of local systems on loci of d-elliptic abelian surfaces

We consider the loci of d-elliptic curves in $M_2$, and corresponding loci of d-elliptic surfaces in $A_2$. We show how a description of these loci as quotients of a product of modular curves can be used to calculate cohomology of natural local systems on them, both as mixed Hodge structures and $\ell$-adic Galois representations. We study in particular the case d=2, and compute the Euler characteristic of the moduli space of n-pointed bi-elliptic genus 2 curves in the Grothendieck group of Hodge structures.Comment: 15 pages, complete re-write of earlier versio

Factor maps between tiling dynamical systems

We show that there is no Curtis-Hedlund-Lyndon Theorem for factor maps between tiling dynamical systems: there are codes between such systems which cannot be achieved by working within a finite window. By considering 1-dimensional tiling systems, which are the same as flows under functions on subshifts with finite alphabets of symbols, we construct a `simple' code which is not `local', a local code which is not simple, and a continuous code which is neither local nor simple.Comment: 8 page