Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Springer eBooks

The Language of Hilbert Space

Stephen Bruce Sontz

Published Jan 1, 2020• 0 citations
Publisher
DOI
10.1007/978-3-030-40767-4_9

Related papers

Is the Hilbert Space Language Too Rich?

Marian Kupczyński

Springer eBooks•Jan 1, 1978•3 citations

Is the Hilbert space language too rich?

Marian Kupczyński

International Journal of Theoretical Physics•Sep 1, 1974•8 citations

A Primer on Hilbert Space Theory

Carlo Alabiso, Ittay Weiss

UNITEXT for physics•Oct 8, 2014•9 citations

Signal detection theory in Hilbert space

Marcus Vinícius C. Baldo

The Hilbert space formalism is a powerful language to express many cognitive phenomena. Here, relevant concepts from signal detection theory are recast in that language, allowing an empirically testable extension of the quantum probability formalism to psychophysical measures, such as detectability and discriminability.

Behavioral and Brain Sciences•May 14, 2013•2 citations

QPEL: Quantum Program and Effect Language

Robin Adams

We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how semantics may be given in terms of state-and-effect triangles, a categorical setting that allows semantics in terms of Hilbert spaces, C*-algebras, and other categories. We prove soundness and completeness results that show the derivable judgements are exactly those provable in all state-and-effect triangles.

arXiv:1412.8543•Electronic Proceedings in Theoretical Computer Science•Dec 28, 2014•5 citations

Rudiments of Hilbert Space Theory

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Theoretical and mathematical physics•Jan 1, 2016•0 citations
We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how semantics may be given in terms of state-and-effect triangles, a categorical setting that allows semantics in terms of Hilbert spaces, C*-algebras, and other categories. We prove soundness and completeness results that show the derivable judgements are exactly those provable in all state-and-effect triangles.