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

TL;DR

This paper explores how to implement and transform frame perspectives in quantum process matrices, connecting coordinate parametrizations with spacetime representations and analyzing their operational implications.

Contribution

It introduces a unified view of causal reference frames and time-delocalized subsystems as perspective-neutral objects, and shows how perspectives can be unitarily transformed.

Findings

Explicit maps for perspective transformation in the quantum switch

Unitary transformations can reshuffle past and future perspectives

Extending processes with quantum reference frames enables perspective relations

Abstract

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.