The causal order of events need not be fixed: whether a bus arrives before or after another at a certain stop can depend on other variables-like traffic. Coherent quantum control of causal order is possible too and is a useful resource for several tasks. However, quantum control implies that a controlling system carries the which-order information-if the control is traced out, the order of events remains in a probabilistic mixture. Can the order of two events be in a pure superposition, uncorrelated with any other system? Here we show that this is not possible for a broad class of processes: a pure superposition of any pair of Markovian, unitary processes with equal local dimensions and different causal orders is not a valid process, namely it results in non-normalised probabilities when probed with certain operations. The result imposes constraints on novel resources for quantum information processing and on possible processes in a theory of quantum gravity.
CITATION STYLE
Costa, F. (2022). A no-go theorem for superpositions of causal orders. Quantum, 6, 663. https://doi.org/10.22331/Q-2022-03-01-663
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