Optimization of distributed EPR entanglement generated between two Gaussian fields by the modified steepest descent method

TL;DR

This paper optimizes the entanglement generated in a dual-NOPA quantum network using a modified steepest descent method to enhance EPR-like entanglement through a static optical network.

Contribution

It introduces a novel optimization approach for passive optical networks to maximize entanglement in a dual-NOPA system.

Findings

The optimized network configuration yields stronger EPR entanglement.

The method effectively decomposes the unitary matrix into implementable optical components.

Enhanced entanglement is achieved with a static passive network.

Abstract

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 $6 \times 6$ 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.