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.
Highlights
Quantum superpositions can be viewed as generalisations of classical probabilities: if classically we can be uncertain between two alternatives, assigning to each a probability, quantumly we should be able to consider a superposition of the two, replacing probabilities with complex amplitudes
Fabio Costa: f.costa@uq.edu.au this question appears problematic because, unlike classical probabilities, quantum superpositions have no clear interpretation in terms of subjective lack of knowledge
We show that for unitary, Markovian processes where all systems have equal dimension superpositions of two different causal orders are not possible, in the sense that they do not constitute valid, deterministic processes
Summary
Quantum superpositions can be viewed as generalisations of classical probabilities: if classically we can be uncertain between two alternatives, assigning to each a probability, quantumly we should be able to consider a superposition of the two, replacing probabilities with complex amplitudes. Feynman’s sum-over-histories approach famously leverages this intuition [1] Despite this view, one typically considers superpositions of states, whereas classical probabilities can be assigned to any logical statement. This question appears problematic because, unlike classical probabilities, quantum superpositions have no clear interpretation in terms of subjective lack of knowledge. The result applies to simple sequences of operations on a target system—as in the switch—showing that an additional system is necessary for performing such operations in an indefinite causal order. It remains an open question whether a superposition is possible under weaker conditions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
