In the kitchen, the sequence of actions is strictly dictated by the recipe: first chop, then fry, and nothing else. In quantum physics, the role of the recipe is played by causality — one event causes another, and they cannot be swapped. But in recent years, theorists have devised clever scenarios where the order of events seems to 'hang' in uncertainty. A photon appears to pass through two devices simultaneously in different sequences, as if a chef could both boil and fry first, without choosing until the very end.
The authors of the new paper asked a simple but profound question: which of these mathematical constructs can be assembled in a real laboratory, without resorting to tricks like discarding failed attempts? They started with a rigorous model of 'causal boxes' compatible with ordinary spacetime, where events cannot influence each other faster than light. Then they added two natural constraints: each device operates exactly once, and inside a closed laboratory, events always form some local chain, even if the global order is blurred.
This is not just a philosophical exercise. A clear boundary between the realizable and the imaginary helps experimenters avoid chasing ghosts and focus on what can actually be built. Perhaps circuits with a controlled order will become the foundation of future quantum computers, where the sequence of operations itself becomes a computational resource, like a chef who can change the recipe mid-cooking to produce dishes impossible under a rigid script.
as written by the authors arXiv:2605.08351
In quantum causality and quantum information, there is a vast landscape of abstract quantum protocols permitting cyclic or non-acyclic causal structures between operations, including frameworks for indefinite causal order and higher-order quantum processes such as process matrices. A longstanding open question is what is the largest class of abstract processes that admit physical realisations without post-selection. In this work, we provide a rigorous answer using a top-down approach grounded in relativistic causality principles. Building on the framework of causal boxes, which characterise the most general quantum information-processing protocols compatible with fixed background spacetimes, we formalise additional constraints (Acting Once + Local Order) capturing the closed-laboratory assumptions of the process matrix framework at a fine-grained spacetime level. We prove that any protocol in a classical acyclic spacetime satisfying these conditions is behaviourally equivalent to a quantum circuit with quantum control of causal order (QC-QC), providing a top-down derivation of QC-QCs from physical principles. Our results show that QC-QCs constitute precisely the class of higher-order quantum processes, including those with indefinite order, that can be physically realised within classical spacetime, ruling out more general non-causal processes under the closed-labs assumption. This clarifies the relationship between abstract higher-order process matrix frameworks and experimentally accessible quantum protocols, as well as the interplay between coarse-grained cyclic and fine-grained acyclic operational causal structures. We also develop characterisation techniques for process box protocols that lead to new causality-based open questions concerning spacetime quantum protocols and relativistic quantum experiments.
The idea of indefinite causal order resembles a situation where two people simultaneously say 'after you' to each other at a door, but at the quantum level, such 'hesitation' can be harnessed for computation.
In Ted Chiang's novella 'Story of Your Life' (adapted into the film 'Arrival'), an alien language alters the perception of time, allowing one to see the past and future simultaneously — much like quantum circuits with unfixed order juggle causality.