A no-go theorem for superpositions of causal orders

Abstract

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.

6+4 pages, two pictures, final version

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Cited by in corpus (3)

• Quantum chicken-egg dilemmas: Delayed-choice causal order and the reality of causal non-separability
• Quantifying Causal Influence in Quantum Mechanics
• Causality in a qubit-based quantum switch