Quantum information effects

Chris Heunen, Robin Kaarsgaard

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We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including measurement. We provide universal categorical constructions that semantically interpret this arrow metalanguage with choice, starting with any rig groupoid interpreting the reversible base language. Several properties of quantum measurement follow in general, and we translate (noniterative) quantum flow charts into our language. The semantic constructions turn the category of unitaries between Hilbert spaces into the category of completely positive trace-preserving maps, and they turn the category of bijections between finite sets into the category of functions with chosen garbage. Thus they capture the fundamental theorems of classical and quantum reversible computing of Toffoli and Stinespring.
Original languageEnglish
Article number2
JournalProceedings of the ACM on Programming Languages
Issue numberPOPL
Pages (from-to)1-27
Publication statusPublished - 12. Jan 2022
Externally publishedYes
Event49th ACM Symposium on Principles of Programming Languages - Philadelphia, United States
Duration: 16. Jan 202222. Jan 2022


Conference49th ACM Symposium on Principles of Programming Languages
Country/TerritoryUnited States

Bibliographical note

Funding information: This material is based upon work supported by the Engineering and Physical Sciences Research
Council Fellowship No. EP/R044759/1, and the Independent Research Fund Denmark under DFFInternational Postdoc Fellowship No. 0131-00025B.


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