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arXiv:2409.18436 · Physical Review A

Polarization-entanglement dynamics in optical fibers: Mitigating decay in the non-Markovian regime with dynamical decoupling

Pratik J. Barge, Arshag Danageozian, Manish K. Gupta, Brian T. Kirby, Hwang Lee

Published Feb 3, 2025• 2 citations
arXivHTMLPDF

Abstract

Future distributed quantum systems and networks are likely to rely, at least in part, on the existing fiber infrastructure for entanglement distribution; hence, a precise understanding of the adverse effects of imperfections in optical fibers on entanglement is essential to their operation. Here, we consider maximally entangled polarization qubits and study the decay of the entanglement caused by spatial fluctuations in the refractive index of optical fibers. We study this entanglement dynamics using the spin-boson model and numerically solve our system of equations using the hierarchical equations of motion (HEOM) formalism. We show that within the range of practically relevant system parameters, our developed model exhibits both Markovian and non-Markovian entanglement decay behavior. Further, to counter the observed entanglement decay, we propose the implementation of dynamical decoupling in optical fibers using spaced half waveplates. In particular, we numerically model the time-dependent Hamiltonians of the Carr-Purcell-Meiboom-Gill and Uhrig dynamical decoupling schemes and show a reduced rate of entanglement decay even with sparsely spaced half waveplates along the length of optical fiber. Finally, we evaluate the performance of these two schemes in multiple system configurations.

DOI
10.1103/physreva.111.023501

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Future distributed quantum systems and networks are likely to rely, at least in part, on the existing fiber infrastructure for entanglement distribution; hence, a precise understanding of the adverse effects of imperfections in optical fibers on entanglement is essential to their operation. Here, we consider maximally entangled polarization qubits and study the decay of the entanglement caused by spatial fluctuations in the refractive index of optical fibers. We study this entanglement dynamics using the spin-boson model and numerically solve our system of equations using the hierarchical equations of motion (HEOM) formalism. We show that within the range of practically relevant system parameters, our developed model exhibits both Markovian and non-Markovian entanglement decay behavior. Further, to counter the observed entanglement decay, we propose the implementation of dynamical decoupling in optical fibers using spaced half waveplates. In particular, we numerically model the time-dependent Hamiltonians of the Carr-Purcell-Meiboom-Gill and Uhrig dynamical decoupling schemes and show a reduced rate of entanglement decay even with sparsely spaced half waveplates along the length of optical fiber. Finally, we evaluate the performance of these two schemes in multiple system configurations.
One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence, to protect photonic qubits from dephasing, by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along realistic lengths of optical fiber and study preservation of polarization qubits through such fibers enhanced with Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. This technique can maintain photonic qubit coherence at high fidelity, making a step toward achieving scalable and useful quantum communication with photonic qubits.
One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence, to protect photonic qubits from dephasing, by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along realistic lengths of optical fiber and study preservation of polarization qubits through such fibers enhanced with Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. This technique can maintain photonic qubit coherence at high fidelity, making a step toward achieving scalable and useful quantum communication with photonic qubits. © 2012 American Physical Society.
In this research work, I have derived analytical models for decoherence of quantum states of light and developed techniques based on Dynamical Decoupling (DD) to preserve the quantum state of polarization qubit and Orbital Angular Momentum (OAM) qudit in single-mode, multi-mode and specialized optical fibers. In subsequent work, I have derived the analytical model for decoherence of an entangled state in an optical fiber to show that such a decoherence causes loss of entanglement. I also showed that such states can be preserved with DD. In Chapter 1, I have introduced the subject of a quantum computer and its relation to quantum communication. I give a brief overview of fundamental concepts and tools required to understand the subject matter. In Chapter 2, I discuss optical fibers from the perspective of the electromagnetic wave in a waveguide and explain the modes in an optical fiber. Later, I explain about the sources of noise or refractive index fluctuation in an optical fiber and show how to numerically reproduce a model of an optical fiber. In Chapter 3, I introduce the topic of quantum decoherence and discuss in detail an open-loop control technique called Dynamical Decoupling, that is applied to the system to minimize decoherence. I discuss ideal and nonideal pulse sequences used for suppressing decoherence. In Chapter 4, I derive the analytical model for decoherence of a polarization qubit in a single-mode, multi-mode fiber, and decoherence OAM qudit in specialized multi-mode fiber. In Chapter 5, I introduce the topic of entanglement for the bipartite system and multi-partite system, and a measure called concurrence to quantify the entanglement. I then derive the analytic model for decoherence of a pure entangled state and show that decoherence causes loss of entanglement for the case of a pure and mixed Werner-like state. \break In Chapter 6, I discuss the method of numerical simulation and show by numerical simulation that polarization qubit, OAM qudit and entanglement of polarization qudit can be preserved with dynamical decoupling in an optical fiber. In Chapter 7, I have summarized the results and discuss the scope of future work. In the appendix, I have included additional research work not directly related to the current topic of decoherence in an optical fiber. To summarize my research, I have derived a model for decoherence and then numerically showed that a polarization qubit can be preserved in a single mode and multi-mode optical fiber. I
Recent advances in quantum photonics promise transformative impacts on computing, communication, sensing, and imaging. This thesis explores two areas in photonic quantum technology: polarization entanglement dynamics in optical fibers and low-light imaging. Optical fibers are the most suitable medium for photonic qubits and long-distance entanglement distribution is a critical requirement to realize quantum technologies. We study the decay of polarization-entanglement of the Bell state photons propagating through imperfect optical fibers with spatially fluctuating refractive index. Furthermore, to extend the distribution distance, we propose the use of dynamical decoupling in the optical fiber using half waveplates and show that significant improvement in entanglement protection can be achieved even with sparsely spaced half waveplates along length of optical fiber. In the realm of imaging, traditional methods are often limited by noise, especially at low illumination levels necessary for certain applications. Quantum imaging techniques, utilizing non-classical light fields and spatial correlations, have demonstrated enhanced sensitivity. We demonstrate a novel imaging method based on spatial changes in the quadrature variance of an optical field, enabling effective imaging at extremely low light levels. Finally, we explore the use compressed sampling to minimize measurement requirements for image reconstruction in single-pixel imaging.
We address the issue of dephasing effects in flying polarization qubits propagating through optical fiber by using the method of dynamical decoupling. The control pulses are implemented with half-wave plates suitably placed along the realistic lengths of the single-mode optical fiber. The effects of the finite widths of the wave plates on the polarization rotation are modeled using tailored refractive index profiles inside the wave plates. We show that dynamical decoupling is effective in preserving the input qubit state with the fidelity close to unity when the polarization qubit is subject to the random birefringent noise in the fiber, as well the rotational imperfections (flip-angle errors) due to the finite width of the wave plates.