Cloning and Deleting Quantum Information from a Linear Logical Point of View

EasyChair Preprint 8435, version 2

Abstract

This paper displays a linear sequent calculus in accordance with the no-cloning and no-deleting theorems of quantum computing. The calculus represents operations on matrices in terms of linear sequent rules, satisfing admissibility of cut. It is possible to define a strict monoidal categorical semantics for it using categories generated by finite vector spaces extended with a Kronecker product, which can be viewed as the dual of an approach proposed by Abramsky-Coecke.

Keyphrases: categorical semantics, linear algebra, linear logic, quantum computing

@booklet{EasyChair:8435,
  author    = {Anderson Beraldo-de-Araújo},
  title     = {Cloning and Deleting Quantum Information from a Linear Logical Point of View},
  howpublished = {EasyChair Preprint 8435},
  year      = {EasyChair, 2022}}