A no-go theorem for superpositions of causal orders
Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia
|Published:||2022-03-01, volume 6, page 663|
|Citation:||Quantum 6, 663 (2022).|
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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.
This work shows that, in general, indefinite causal order and quantum superpositions are quite distinct concepts. In particular, when we consider the experiments performed so far, we cannot simply remove the coin flip: it is essential for the whole scheme to be even possible. More generally, this work shows that quantum superpositions of causal orders are not possible, at least in a very broad range of situations. The result provides new tools to investigate indefinite causal order, which will help in the search of novel quantum causal structures.
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