  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.
