Diagnostics of Quantum Entanglement for use in Stable Interferometry in Polarization Maintaining Optical Fiber

Squeezed light is a valuable resource in photonic quantum technology that allows us to surpass the standard quantum limit in certain measurements. This paper discusses the generation of polarization-squeezed entanglement, focusing on the generation of two-mode squeezed states entanglement from a non-linear crystal in the process of squeezing. We also examine the utilization of the GKP code, which encodes quantum information in continuous-variable systems, to provide a framework for using polarization-squeezing in manipulating quantum information in infinite-dimensional spaces. While the GKP code primarily focuses on continuous variables like position and momentum, we show that the principles of encoding and stabilizing quantum information can be extended to other types of quantum states, including polarization-encoded states. The paper aims to explore the general use of polarization squeezing as stabilizing qubits for quantum applications, such as using flying qubits for entanglement resources. We demonstrate the use of Kuramoto oscillators to simulate the use of Phase-insensitive amplification (PIA) on GKP-stabilized qubit nodes to demonstrate a technique for boosting the sensitivity of qubits-as-sensors, for instance, in an interferometer array. The ability to amplify signals between nodes without introducing noise makes PIA an essential tool for advancing our ability to detect subtle changes in stabilized qubits and unlock the potential of their use in quantum sensing technology in diverse sensor scenarios ranging from chiral polarimetry to distributed fiber-based sensing and interferometery using polarization entanglement sources. Of key import here is the means to develop new figures of merit for fiber sensing. To do this a factor, \(\Qoppa_P\) , is used in relation to polarization shifts treated as a Doppler-like Effect in the network Lagrangian framework.