Mach's Principle and Local Causal Structure

Gábor Hofer‐Szabó, Péter Vecsernyés

Mikhail Pavlov

Description / Abstract:This research explores the emergence of indefinite causal order within quantum systems through the lens of the Quantum Switch and Everettian quantum mechanics. By formalizing the concept of discrete P-tacts—primitive process units composed of local unitaries and entangling operations—the work introduces flat acts as fundamental structures representing coherent process sequences. The study develops a graphical framework of P-tact networks to represent superpositions of causal orders, demonstrating how indefinite causal relations can be realized without invoking wavefunction collapse. Experimental implications include connections to EPR experiments, quantum teleportation, and Mach–Zehnder interferometry. This approach provides a novel, process-oriented formalism unifying quantum causality, entanglement, and Everettian branching, suitable for applications in quantum information processing and foundational physics.

Zixuan Liu, Ognyan Oreshkov

Processes with indefinite causal order can arise when quantum theory is locally valid and they allow accomplishing new informational tasks. Despite recent progress, the correlations allowed in such processes have not been clearly understood. Here, we propose to study the constraints on information exchange through such processes in a paradigm of locally sequential operations. In this paradigm, we identify an information-theoretic principle constraining the correlations, termed parity erasure, which follows from the local validity of causality. We show that this principle completely characterizes the local-tomography representation of higher-order processes with indefinite causal order: among all multipartite channels, the ones describing valid higher-order processes are those and only those whose input-output correlations respect parity erasure. This approach reveals a fundamental property of information exchange in scenarios with indefinite causal structure and opens a new arena for exploring their potential applications.

Gábor Hofer‐Szabó, Péter Vecsernyés

Zhian Jia, Min-Jeong Song, Dagomir Kaszlikowski

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.

J. S. Bell