Information and Physics II
According to the physicist Ralf Landauer, “information is physical:” Although information theory, as founded by Shannon, treats information as an abstract concept independent of its physical realization — and has been very successful with this —, it is nevertheless true that any information representation, treatment, or transmission process is ultimately physical and must be understood as being physical. This insight has consequences of two types, the derivation, understanding, and application of which is in the focus of the proposed project: On the one hand, physical facts have implications for information treatment; on the other, the point of view of information can allow us to better understand physical laws. We have had in our research experience with both these aspects of the interplay between information and physics, and we plan to continue working in both directions; this has, in our experience, turned out to be very fruitful. Following Landauer’s reasoning, we conclude that physical laws are relevant in the context of infor- mation processing — some more than others. For instance, the laws of thermodynamics put limits on the miniaturization and speed of computing devices. On the more constructive side, the laws of quantum physics can enable more secure cryptographic protocols, faster computing, or a reduction of the required communication for distributed tasks. It is the overarching goal of our research to understand, from the standpoint of information, the relevant physical laws more deeply (or at least differently) and, in turn, their implications for information treatment.We propose to continue our work from the first project phase, which led to applications of physical laws for information treatment, e.g., cryptography, and new insight into physical phenomena such as non-locality, when analyzed from the informational point of view. Continuing in the same spirit, but with the intention of broadening our scope, we propose to investigate questions in the intersection of quantum physics, thermodynamics, information theory, cryptography, and communication as well as computational complexity. Specifically, we propose four sub-projects devoted to the following subjects and questions. Non-locality: distillation, information principles, and cryptography. Understand the proper- ties and the uses of non-local correlations — quantum and beyond — such as the possibility of distillation in the two- and more-party scenarios, find an information-theoretic characterization of quantum as opposed to “super-quantum” correlations, and use the correlations for cryptographic tasks such as efficient causal key distribution (CKD) or two- and multi-party tasks like oblivious transfer, bit commitment, or secure function evaluation. Quantifying and measuring non-locality and contextuality in theory and experiment. Determine the communication complexity of quantum primitives such as quantum channels or quantum entanglement in the asymptotic setting. Apply the derived techniques to both theoretical and experimental data. Correlations and signaling without causal order. Understand the consequences of dropping the condition that some (physical) theory, such as classical probability theory or quantum theory, be valid globally instead of only locally. What are the kinds of correlations, signaling or not, that become compatible with the local validity of the underlying theory? Understand the exact connections between signaling correlations and non-locality, in particular the analogy in the form of the apparent differences between the two- and multi-partite cases. Randomness, entropy, and Kolmogorov thermodynamics. Understand thermodynamic concepts and statements, such as the possibility of work extraction from a physical system or the second law of thermodynamics, from the computational, algorithmic point of view, invoking Kolmogorov complexity or finite-automata theory for modeling the entities actually extracting the work (quite similarly to Maxwell’s famous “demon”) with the goal of obtaining constructive results.We expect the outcomes to have an impact in all fields involved — as it has often been the case in our research. More precisely, it lies in the nature of the proposed project that engineering characteristics and methodology — “what can we do efficiently?” — are combined with science aspects — “can we understand the underlying phenomena better?”.