Indefinite Causal Structures in Quantum Systems

Classical physics presumes a fixed order of events: causes precede effects along a well‐defined temporal axis. Quantum mechanics, however, permits scenarios in which the causal order of operations becomes a quantum degree of freedom. In such settings, two or more operations may act in a superposition of different orders, giving rise to processes that cannot be embedded in any definite causal sequence. These so-called indefinite causal structures challenge our notions of time, signalling and the very fabric of spacetime. At the heart of this field lies the quantum switch, a higher-order transformation that coherently controls the sequence in which quantum channels are applied. Theoretical frameworks based on process matrices and generalised causal models formally capture these phenomena, leading to new resource theories of causality. Indefinite causal structures have been shown to violate causal inequalities—constraints analogous to Bell inequalities but for temporal order—and to enable tasks such as perfect quantum communication through otherwise zero-capacity channels. Beyond fundamental implications for quantum gravity and the nature of time, these advances hold promise for enhanced metrology, communication and computation, where the superposition of causal orders can outperform any fixed-order protocol.

Research from Nature Portfolio

Recent studies have provided device-independent tools to certify indefinite causal order in implementations of the quantum switch. An experiment introduced a causal inequality tailored to a scenario involving an auxiliary spacelike-separated observer, enabling the detection of indefinite order without assumptions on the internal workings of devices. This work establishes a robust test for causal nonseparability akin to Bell tests for nonlocality. Another investigation has explored entanglement of temporal orders by placing a massive object in spatial superposition, thereby entangling the ordering of two time-like events. That study demonstrated the violation of a temporal Bell-type inequality and highlighted the incompatibility of classical causal descriptions with quantum-enhanced gravitational scenarios.

Indefinite Causal Structures in Quantum Systems publication trend

The graph below shows the total number of articles in indefinite causal structures in quantum systems across all publications each year (not limited to Nature Index journals).

Technical terms

Indefinite causal order: A quantum process in which the sequence of operations is not fixed but exists in a coherent superposition.

Quantum switch: A higher-order operation that places two or more quantum channels in a superposition of different orders.

Process matrix: A mathematical object describing multipartite quantum processes without assuming a global causal structure.

Causal nonseparability: The property of a process that cannot be decomposed into a mixture of definite causal orders.

Causal inequality: A constraint on correlations that holds when events obey a fixed causal order, violated by processes with indefinite order.

References

1. Device-independent certification of indefinite causal order in the quantum switch. Nature Communications (2023).
2. Quantum causal modelling. New Journal of Physics (2016).
3. Bell’s theorem for temporal order. Nature Communications (2019).
4. Indefinite causal order enables perfect quantum communication with zero capacity channels. New Journal of Physics (2021).
5. Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics. Quantum (2019).