CAREER: A Physical Understanding of Secrecy

从情报简报到电子商务，几乎社会各个层面都依赖于私人信息的安全传输。当两个或更多方共享秘密数据时，他们通常可以执行某些操作来加强其信息安全。例如，有时向不想要的窃听者泄露部分信息实际上可以提高整体安全性。这个项目寻求开发一幅关于当受信任的各方操纵他们的数据并相互公开共享他们的部分信息时，保密如何演变的量化图景。通过使用最近发展起来的研究量子纠缠和纠缠变换理论的技术，将采用一种新的方法来解决这个问题。保密的概念将被置于与量子纠缠相同的基本水平上，因为两者都将被视为宝贵的物理资源，可以被操纵并用于各种信息处理任务。研究经典保密性和量子纠缠之间的联系不仅将为量子力学和经典信息论之间的统一提供一个新的水平，而且还将为量子物理和经典物理学的不同之处提供一个新的视角。最终，该项目对经典保密性的深入理解将导致改进的安全分析和安全传输信息的新方法。本研究计划研究量子信息理论和经典密码学中的基本问题。典型的量子密钥分发(QKD)协议(就像商业QKD机器使用的协议)由两个独立的阶段组成--称为Alice和Bob--他们使用量子通道在它们之间交换量子信息。然而，在这个过程中，一个名叫夏娃的窃听者可能会与他们的状态相互作用，因此所有三个系统都可以用联合量子态ABE来描述。最终，各方对各自的系统进行测量，并获得测量结果，即经典数据。但由于量子力学的不确定性，这些测量数据只能用一些三方概率分布PABE来描述。QKD协议的第二阶段是纯经典的，现在由Alice和Bob使用本地操作和公共通信来将分发PABE转换为秘密密钥状态，这些密钥状态是Alice和Bob之间共享的完全相关的比特，但对Eve完全隐藏。这个过程被称为公钥协议，或秘密密钥蒸馏。使用密钥状态，Alice和Bob将能够秘密传输来自Eve的数据，而不管她的计算能力如何。由于使用公钥协议，可以将分发PABE转换为秘密密钥状态，因此分发PABE被称为具有“秘密相关性”。共享秘密关联的经典系统与共享纠缠的量子系统的行为非常相似。特别是，量子纠缠和秘密关联都可以通过局部物理处理和全球经典通信来转换、退化和增强。在这个项目中，将构建一个适用于研究秘密关联的最一般物理操作的数学框架，这是目前研究文献中所缺乏的。在这个框架内，将开发新的分析工具来研究密钥蒸馏的关键问题，以及何时可以将一种类型的秘密关联转换为另一种类型的更广泛的问题。一个特别的重点将是产生新的保密性、单调和不完全依赖于信息理论量的措施，例如信息熵和互信息。此外，还将介绍受量子信息论中类似原语启发的新的密码学范例，如随机纠缠蒸馏和纠缠梳理。该项目的一个基本目标是将经典保密和量子纠缠统一为物理类比。在这样的对应下，纠缠理论中的已知技术和结果可以应用于保密研究，反之亦然。

From intelligence briefings to ecommerce, nearly all levels of society rely on the secure transmission of private information. When two or more parties share secret data, often there are certain actions they can perform to strengthen their information security. For example, sometimes revealing partial information to an unwanted eavesdropper can actually improve the overall security. This project seeks to develop a quantitative picture of how secrecy evolves as the trusted parties manipulate their data and publicly share part of their information with one another. A novel approach to this problem will be adopted through the use of recently developed techniques in the study of quantum entanglement and the theory of entanglement transformations. The notion of secrecy will be placed on the same fundamental level as quantum entanglement in that both will be viewed as precious physical resources that can be manipulated and used for various information processing tasks. Investigating the connection between classical secrecy and quantum entanglement will not only offer a new level of unification between quantum mechanics and classical information theory, but it will also yield a fresh perspective on how quantum and classical physics differ. Ultimately, the deeper understanding of classical secrecy developed in this project will lead to improved security analysis and new methodologies for securely transmitting information.This research program investigates fundamental questions in quantum information theory and classical cryptography. A typical quantum key distribution (QKD) protocol (like those employed by commercial QKD machines) consists of two separate phases - called Alice and Bob - who use a quantum channel to exchange quantum information between them. However, in this process an eavesdropper - named Eve - may interact with their state so that all three systems are described by the joint quantum state ρABE. Eventually the parties measure their respective systems and obtain measurement outcomes, i.e. classical data. But due to the indeterminism of quantum mechanics, this measurement data can only be described by some tripartite probability distribution PABE. The second phase of the QKD protocol is purely classical and now consists of Alice and Bob using local operations and public communication to convert the distribution PABE into secret key states, which are perfectly correlated bits shared between Alice and Bob, yet completely hidden from Eve. This process is known as public key agreement, or secret key distillation. Using secret key states, Alice and Bob will be able to transmit data secretly from Eve, regardless of her computational power. The distribution PABE is said to possess "secret correlations" since using public key agreement, it can be converted into secret key states. Classical systems that share secret correlations behave remarkably similar to quantum systems that share entanglement. In particular, both quantum entanglement and secret correlations are capable of being transformed, degraded, and enhanced through local physical processing and global classical communication. In this project, a mathematical framework will be constructed that is suitable for studying the most general physical manipulations of secret correlations, something currently lacking in the research literature. Within this framework, new analytic tools will be developed to study the crucial problem of secret key distillation and the broader question of when one type of secret correlations can be transformed into another. A particular focus will be on generating new secrecy monotones and measures that do not rely exclusively on information-theoretic quantities such as entropy and mutual information. Additionally, novel cryptographic paradigms will be introduced that are inspired by similar primitives in quantum information theory, such as random entanglement distillation and entanglement combing. An underlying goal of this project will be to unify classical secrecy and quantum entanglement as physical analogs. Under such a correspondence, known techniques and results in entanglement theory can be applied in the study of secrecy, and vice versa.