Banerjee Pradeep Kr
Institute for Data Science Foundations, Blohmstraße 15, 21079 Hamburg, Germany.
Entropy (Basel). 2025 Jan 1;27(1):29. doi: 10.3390/e27010029.
The problem of constructing information measures with a well-defined interpretation is of fundamental significance in information theory. A good definition of an information measure entails certain desirable properties while also providing answers to operational problems. In this work, we investigate the properties of the unique information, an information measure that quantifies a deviation from the Blackwell order. Beyond providing an accessible introduction to the topic from a channel ordering perspective, we present a novel resource-theoretic characterization of unique information in a cryptographic task related to secret key agreement. Our operational view of unique information entails rich physical intuition that leads to new insights into secret key agreement in the context of non-negative decompositions of the mutual information into redundant and synergistic contributions. Through this lens, we illuminate new directions for research in partial information decompositions and information-theoretic cryptography.
构建具有明确定义解释的信息度量问题在信息论中具有根本重要性。一个好的信息度量定义需要具备某些理想属性，同时还要为实际问题提供答案。在这项工作中，我们研究独特信息的属性，独特信息是一种量化与布莱克威尔序偏离程度的信息度量。除了从信道排序角度对该主题进行通俗易懂的介绍外，我们还在与秘密密钥协商相关的密码任务中给出了独特信息的一种新颖的资源理论表征。我们对独特信息的实际观点蕴含丰富的物理直觉，这为在互信息分解为冗余和协同贡献的非负分解背景下的秘密密钥协商带来了新见解。通过这个视角，我们阐明了部分信息分解和信息论密码学研究的新方向。
