Optimization of distributed EPR entanglement generated between two Gaussian fields by the modified steepest descent method
Zhan Shi, Hendra I. Nurdin · 2015
Recent theoretical investigations on quantum coherent feedback networks have found that with the same pump power, the Einstein-Podolski-Rosen (EPR)-like entanglement generated via a dual nondegenerate optical parametric amplifier (NOPA) system placed in a certain coherent feedback loop is stronger than the EPR-like entangled pairs produced by a single NOPA.In this paper, we present a linear quantum system consisting of two NOPAs and a static linear passive network of optical devices.The network has six inputs and six outputs, among which four outputs and four inputs are connected in a coherent feedback loop with the two NOPAs.This passive network is represented by a 6 × 6 complex unitary matrix.A modified steepest descent method is used to find a passive complex unitary matrix at which the entanglement of this dual-NOPA network is locally maximized.Here we choose the matrix corresponding to a dual-NOPA coherent feedback network from our previous work as a starting point for the modified steepest descent algorithm.By decomposing the unitary matrix obtained by the algorithm as the product of so-called two-level unitary matrices, we find an optimized configuration in which the complex matrix is realized by a static optical network made of beam splitters.