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Typing Quantum Superpositions and Measurement

Authors: Alejandro Díaz-Caro; Gilles Dowek;

Typing Quantum Superpositions and Measurement

Abstract

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis.

Countries
Argentina, France
Keywords

LAMBDA CALCULUS, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], lambda-calculus, quantum computing, QUANTUM COMPUTING, algebraic linearity, ALGEBRAIC LINEARITY, linear logic, https://purl.org/becyt/ford/1.2, measurement, https://purl.org/becyt/ford/1, LINEAR LOGIC

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    popularity
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Top 10%
Average
Top 10%
Green
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