Frame perspectives for process matrices: from coordinate parametrization to spacetime representation

Quantum Physics [Submitted on 3 Apr 2026] Frame perspectives for process matrices: from coordinate parametrization to spacetime representation Luca Apadula, Alexei Grinbaum, Časlav Brukner We study how to implement and transform frame perspectives for quantum processes in the process-matrix formalism. We argue that, for pure processes, the causal reference frames (CRF)and time-delocalized subsystems (TDS) formalisms should be understood as coordinate parametrizations of a single perspective-neutral higher-order object. A genuine perspective arises when one endows the process with additional frame data by choosing an operational foliation into circuit fragments (events). With this distinction, existing no-go results acquire a clear scope: they rule out unitary transformations that preserve time foliation, attempting to switch perspectives while keeping the fragment boundaries -- hence the global past/future partition -- fixed. Focusing on the quantum switch, we construct explicit maps that transform perspectives unitarily at the price of reshuffling the notions of past and future. We then show that unitary transformations between perspectives can also be achieved in a different way, namely by extending the process with subsystems that define quantum reference frames and provide a shared spatiotemporal scaffold. In this extended setting, complementary CRF/TDS perspectives become unitarily related while preserving global past and future. We discuss how this frame-perspectival approach informs the broader question of empirical realizability of abstract process matrices. Comments: 14 pages, 40 figures Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2604.02873 [quant-ph]   (or arXiv:2604.02873v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.02873 Focus to learn more Submission history From: Luca Apadula [view email] [v1] Fri, 3 Apr 2026 08:39:58 UTC (2,761 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: gr-qc References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)