FET: Small: Theoretical Foundations and Applications of High Dimensional Quantum Communication

量子密码学承诺未来的通信基础设施不仅在今天是安全的，而且在未来的技术突破中也是安全的，例如大规模量子计算机的发展。然而，尽管有这种巨大的潜力，但在这项技术得到广泛采用之前，必须克服两个关键缺点。首先是对噪音的容忍，其次是效率。正如初步证据显示的那样，高维量子态是解决这两个问题的首选方案，然而，对为什么会出现这种情况、它实际发生的时间以及如何有效地利用这种力量的确切研究仍然是悬而未决的问题。这个项目加深了我们对高维量子通信的理解，开发了回答这些问题的见解，同时还发现了新的应用和协议，以更容易、更有效地利用高维量子通信系统的力量。此外，该项目为本科生研究人员提供了参与其中的机会，并为量子技术本科教育提供了新的材料，这对未来的劳动力和研究至关重要。该项目的最终目标是阐明高维量子保密通信在包括量子密钥分发在内的应用中的理论基础。PI正在开发利用高维量子态的新型量子协议，同时还开发必要的信息理论工具来分析它们的行为和安全性。考虑了各种噪声场景，以及允许在各种操作场景中优化性能的新型自适应协议。本项目中发展的信息论方法，使我们能够证明这些新协议的安全性，并在量子信息科学中的其他研究领域也有广泛的应用。此外，这些新协议比目前的工作具有许多优势，同时也允许我们进一步探索量子安全通信的基础。高维状态的新密码应用也在调查中，在各种安全模型中，创造了理论上的见解，也可能是更实用的系统。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum cryptography promises a future communication infrastructure that is secure not only today, but also against future technological breakthroughs, such as the development of large-scale quantum computers. However, despite this great potential, there are two critical shortcomings that must be overcome before this technology can see wide-scale adoption. First is noise tolerance and the second is efficiency. High-dimensional quantum states are a prime candidate to solve both problems as preliminary evidence shows, however an exact study of why this true; when it actually occurs; and how to effectively harness this power are still unanswered questions. This project deepens our understanding of high-dimensional quantum communication, develops insights to answer these questions, while also discovering new applications and protocols to more readily, and more effectively, harness the power of higher-dimensional quantum communication systems. Furthermore, this project provides opportunities for undergraduate researchers to become involved and also provides new material for undergraduate education in quantum technology, vital to the future workforce and research.This project's ultimate goal is to shed light on the theoretical foundations of high-dimensional quantum secure communication in applications including, and beyond, quantum key distribution. The PI is developing novel quantum protocols utilizing high-dimensional quantum states, while also developing the necessary information theoretic tools needed to analyze their behavior and security. Various noise scenarios are considered, along with novel adaptive protocols allowing for optimized performance over a variety of operational scenarios. The information theoretic methods developed in this project, allowing us to prove security of these new protocols, also have broad application to other research areas within quantum information science. Furthermore, these new protocols hold numerous advantages over current work, while also allowing us to probe further at the foundations of quantum secure communication. New cryptographic applications of high-dimensional states are also under investigation, in a variety of security models, creating theoretical insights, and also potentially more practical systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.