A no-go theorem for superpositions of causal orders
- URL: http://arxiv.org/abs/2008.06205v3
- Date: Tue, 22 Feb 2022 06:14:49 GMT
- Title: A no-go theorem for superpositions of causal orders
- Authors: Fabio Costa
- Abstract summary: Quantum control implies that a controlling system carries the which-order information.
Can the order of two events be in a pure superposition, uncorrelated with any other system?
A pure superposition of any pair of Markovian, unitary processes with equal local dimensions and different causal orders is not a valid process.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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