A linear-typed higher-order language realises indefinite causal orders on general quantum channels (including measurements), with soundness in Caus[CPM] and expressivity covering all first-order channels plus a large class of QC-QCs.
Finn Voichick, Liyi Li, Robert Rand, and Michael Hicks
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Higher-Order Programs with Indefinite Causal Orders: a Linear Approach to Coherent Control of Quantum Processes
A linear-typed higher-order language realises indefinite causal orders on general quantum channels (including measurements), with soundness in Caus[CPM] and expressivity covering all first-order channels plus a large class of QC-QCs.