Agency under indefinite causality: operational eternalism in higher-order quantum theory

TL;DR

The paper addresses the tension between operational quantum theory and dynamical spacetime physics in the context of indefinite causality, arguing that this tension cannot be reconciled if both pictures are fundamental. It proposes operational eternalism, a global, data-centric view in which inputs/outputs are primitive and agency emerges as perspectival groupings of data described by higher-order processes and supermaps $W$, as exemplified by the quantum switch with a control qubit in superposition. A key contribution is the formalization of observerhood through a friendliness criterion, clarifying when different agents’ perspectives can be meaningfully compared (e.g., in Wigner-type scenarios) and showing that some noncausal settings are operationally meaningful yet not realizable in spacetime without introducing additional observers (e.g., Lugano process). The work suggests a paradigm shift away from spacetime-based ontologies toward an information-theoretic, metageometrical account of causality and agency, with implications for the foundations of quantum gravity and the role of observers.

Abstract

After two decades of research on indefinite causality, a philosophical lesson emerges: the tension between operational quantum theory and dynamical spacetime physics is unbridgeable if one believes both types of theories to be fundamental. We interpret this tension through operational eternalism, a stance analogous to the block-universe view but applied to information rather than geometry. Inputs and outputs are primary givens, while agents are secondary constructs arising from specific groupings of data. Agency is perspectival: from Alice's perspective Bob may not qualify as an observer, and vice versa. These results redefine the observer in the operational approach as a tool to avoid non-causality. They also provide a criterion for Wigner's friends as a class of causally compatible agents.

Figures (9)

• Figure 1: The quantum switch achieves an indefinite causal order LoizeauAG. Depending on the state of the control qubit $c$ in the computational basis, the target system $t$ will follow either path $C_0$ or $C_1$. Conventionally, $C_0$ is in Alice's lab and $C_1$ in Bob's. If the control is in a superposition state, the order of passage is indefinite.
• Figure 2: Higher-order processes are generalized processes in a global Hilbert space that includes as subspaces the agents' input and output Hilbert spaces. The agents' channels are transformed by a superchannel in this global space taranto2025higherorderquantumoperations.
• Figure 3: Process matrix oreshkov_quantum_2012 in the higher-order process formalism taranto2025higherorderquantumoperations. Alice's and Bob's channels relate their respective inputs and outputs, while the higher-order supermap or superchannel $W$ acts on these channels without placing them in any particular time order.
• Figure 4: The quantum switch in a circuit representation from Bob's perspective Oreshkov2018. Bob's operation $U_B$ is localized in time, while Alice's input and output subspaces encompass several time steps. Her operation $U_A$ is applied only once but its temporal location is indefinite (see Section \ref{['sect3']} for the discussion). David and Charlie are superfluous agents added in the common past and future of the setting. They only have an input and an output, respectively, and are equivalent to the observers $P$ and $F$ in the cyclic diagram of the quantum switch in Figure \ref{['fig:cyclic']} (see Section \ref{['sect:obs_eternalism']} for the discussion).
• Figure 5: In his laboratory, the external observer Bob can measure the joint quantum state of the internal observer Alice and the quantum system, while Alice in her laboratory measures only the quantum system. Under operational eternalism the subspace of the quantum system is assumed to be accessible in both labs. Alice is not Bob's friend in the sense of the operational criterion of friendliness in Section \ref{['sect:eternalism']}, because Alice's input and output are time-delocalized in Bob's perspective. In order to communicate their outputs like in the Wigner Friend scenario, Alice and Bob need to align their perspectives. This, however, cannot be achieved via a unitary transformation respecting their local time arrows.