Quantum space-time marginal problem: global causal structure from local causal information

• Published in: New journal of physics Vol. 25; no. 12; pp. 123038 - 123060
• Main Authors: Jia, Zhian, Song, Minjeong, Kaszlikowski, Dagomir
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.12.2023
• Subjects: channel marginal problem; Maximum entropy; maximum entropy principle; Physics; pseudo-density operator; quantum causality; quantum marginal problem; Spacetime; temporal entanglement entropy; temporal quantum correlation
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ad1416

Abstract Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators (PDOs), and quantum causality between the involved events in an experiment is encoded in the corresponding PDO. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the reduced PDOs; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle. The notion of quantum pseudo-channel (QPC) is also introduced and we demonstrate that the QPC marginal problem can be solved by transforming it into a PDO marginal problem via the channel-state duality.