Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
V. Vilasini, Renato Renner
备注：
37+30 pages, 17 figures. v4 is closest to published version. An extra result (Theorem 5.8) included in v2 but not in v1 was found to be partly incorrect, it has been removed and does not impact the main results/conclusions. v4 also includes significant improvements to the framework since v1, in terms of clarity and generality, as well as an additional result about the link to causal boxes
The notions of causality adopted within the quantum information and spacetime physics communities are distinct. Although both notions play a role in physical experiments, their general interplay is little understood in theory. We develop a theoretical framework that connects the two causality notions, while also clearly distinguishing them. The framework describes a composition of quantum operations through feedback loops, and the embedding of the resulting, possibly cyclic information-theoretic structure in an acyclic spacetime structure. Relativistic causality (which forbids superluminal communication) follows as a graph-theoretic compatibility condition between the two structures. Formulating indefinite causal order (ICO) processes in our framework, we shed light on the links between indefinite and cyclic causality, and on questions regarding their physicality. In particular, there are several experiments that claim to implement ICO processes in Minkowski spacetime, presenting an apparent paradox: how can an indefinite information-theoretic causal structure be consistent with a definite spacetime causal structure? We address this through no-go theorems, showing that as a consequence of relativistic causality, (a) realisations of ICO processes necessarily involve the non-localisation of systems in spacetime and (b) will nevertheless admit an explanation in terms of a definite and acyclic causal order process, at a fine-grained level. This fully resolves the apparent paradox and bears implications for the physical interpretation of ICO experiments, and is achieved by introducing the concept of fine-graining that allows causal structures to be analysed at different levels of detail. Our work also sheds light on the limits of quantum information processing in spacetime and on the operational meaning of indefinite causality, within and beyond the context of a fixed spacetime.
Nordita, Stockholm University and KTH Royal Institute of Technology（诺尔迪塔，斯德哥尔摩大学和皇家理工学院）；School of Mathematics and Physics, The University of Queensland（昆士兰大学数学与物理学院）；Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and School of Electrical, Electronic and Mechanical Engineering, University of Bristol（布里斯托大学量子工程技术实验室、H.H.威尔斯物理实验室和电气、电子与机械工程学院）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔国立理工学院、内耳研究所）；University of Vienna, Faculty of Physics, Vienna Doctoral School in Physics, and Vienna Center for Quantum Science and Technology (VCQ)（维也纳大学物理学院、维也纳物理博士学校和维也纳量子科学与技术中心（VCQ））；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所（IQOQI））；Sorbonne Université, CNRS, LIP6（索邦大学、法国国家科学研究中心、LIP6实验室）
Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子理论国际中心）；Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）；Université Grenoble Alpes, Inria（格勒诺布尔阿尔卑斯大学法国国家信息与自动化研究所）
Experimental violation of a Bell-like inequality for causal order
University of Science and Technology of China（中国科学技术大学）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（安徽省量子网络重点实验室，中国科学技术大学）；College of Physics, Guizhou University（贵州大学物理学院）
