A no-go theorem for superpositions of causal orders

TL;DR

This paper proves a fundamental no-go theorem showing that pure superpositions of causal orders cannot exist for a broad class of quantum processes, impacting quantum information and theories of quantum gravity.

Contribution

It establishes that pure superpositions of causal orders are impossible for certain quantum processes, revealing fundamental constraints on quantum control of causality.

Findings

Pure superpositions of causal orders lead to non-normalized probabilities.

The theorem applies to Markovian, unitary processes with equal local dimensions.

Results constrain resources for quantum information and models of quantum gravity.

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.