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arXiv:1510.00707 · Physical Review Applied

Dephasing of Single-Photon Orbital Angular Momentum Qudit States in Fiber: Limits to Correction via Dynamical Decoupling

Manish K. Gupta, Jonathan P. Dowling

Published Jun 24, 2016• 6 citations
arXivHTMLPDF

Abstract

The bit rate for photonic quantum-state transmission can be raised by encoding more than one bit per photon, using multiple temporal, spatial, polarization, and frequency modes and preparing a single photon in a superposition of these modes as a $q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t$. As always, state dephasing limits the performance of such technologies. This study shows that the qudit approach cannot be ramped up to arbitrarily high quantum numbers of orbital angular momentum---but there is a path to passive linear optical elements that can mitigate the inevitable dephasing and keep fidelity high.

DOI
10.1103/physrevapplied.5.064013

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The bit rate for photonic quantum-state transmission can be raised by encoding more than one bit per photon, using multiple temporal, spatial, polarization, and frequency modes and preparing a single photon in a superposition of these modes as a q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t. As always, state dephasing limits the performance of such technologies. This study shows that the qudit approach cannot be ramped up to arbitrarily high quantum numbers of orbital angular momentum---but there is a path to passive linear optical elements that can mitigate the inevitable dephasing and keep fidelity high.
Orbital angular momentum (OAM) of photons provides a promising approach to enhance the capacity, robustness, and functionality of quantum communication systems in optical fibers. With many twist states available, OAM enables high-dimensional encoding, significantly increasing data rates and noise tolerance. This review explores sources, channels, and system architectures for OAM-based quantum communication in fibers. It compares free-space and integrated emitters, discussing in-fiber pair generation and mode conversion pathways that produce fiber-ready single photons and entangled states. For the channels, it details design principles and trade-offs for step-index and ring-core fibers that minimize intermodal coupling and reviews milestones in kilometer-scale single-photon transmission and high-dimensional entanglement transport. On the system side, the review examines coupling, multiplexing, and detection techniques—including mode (de)multiplexers, lanterns, and programmable sorters—and discusses transmission-matrix-based control methods to mitigate dispersion and bending effects. The review concludes with practical guidance and open challenges, such as improving mode selectivity and stability under real-world conditions; developing compact, efficient detectors for many modes; and integrating co-designed error correction schemes. These directions aim to bridge laboratory demonstrations with the deployment of scalable, high-dimensional fiber networks that harness OAM to significantly boost capacity, resilience, and functionality.
Going beyond two-state qubits, $q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}s$ based on quantum states of high dimension constitute a rich resource in quantum information, and their exploitation will play a prominent role in next-generation technologies. Generation and manipulation of qudits have improved strongly over the last decades; their reliable transmission between remote locations remains the central challenge. The authors use an air-core fiber supporting orbital angular momentum (OAM) modes to faithfully transmit qudits. Four OAM quantum states and their superpositions are created, propagated over a 1.2-km fiber, and detected. Moreover, three quantum-key-distribution protocols are implemented.
Optical networks implementing single-qudit quantum gates may exhibit superior properties to those for qubits as each optical element in the network can work in parallel on many optical modes simultaneously. We present a class of such networks that implements in a deterministic and efficient way the quantum Fourier transform (QFT) in an arbitrarily high dimension. These networks redistribute the initial quantum state into the orbital angular momentum (OAM) and path degrees of freedom and offer two modes of operation. Either the OAM-only QFT can be implemented, which uses the path as an internal auxiliary degree of freedom, or the path-only QFT is implemented, which uses the OAM as the auxiliary degree of freedom. The resources for both schemes scale linearly O(d)O(d)O(d) with the dimension ddd of the system, beating the best known bounds for the path-encoded QFT. While the QFT of the orbital-angular-momentum states of single photons has been applied in a multitude of experiments, these schemes require specially designed elements with nontrivial phase profiles. In contrast, we propose a different approach that utilizes only conventional optical elements.
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
Engineering single-photon states endowed with orbital angular momentum (OAM) is a powerful tool for quantum information photonic implementations. Indeed, due to its unbounded nature, OAM is suitable for encoding qudits, allowing a single carrier to transport a large amount of information. Most of the experimental platforms employ spontaneous parametric down-conversion processes to generate single photons, even if this approach is intrinsically probabilistic, leading to scalability issues for an increasing number of qudits. Semiconductor quantum dots (QDs) have been used to get over these limitations by producing on-demand pure and indistinguishable single-photon states, although only recently they have been exploited to create OAM modes. Our work employs a bright QD single-photon source to generate a complete set of quantum states for information processing with OAM-endowed photons. We first study hybrid intraparticle entanglement between OAM and polarization degrees of freedom of a single photon whose preparation was certified by means of Hong–Ou–Mandel visibility. Then, we investigate hybrid interparticle OAM-based entanglement by exploiting a probabilistic entangling gate. The performance of our approach is assessed by performing quantum state tomography and violating Bell inequalities. Our results pave the way for the use of deterministic sources for the on-demand generation of photonic high-dimensional quantum states.