Kindergarten Quantum Mechanics

TL;DR

This paper introduces a visual calculus for quantum mechanics using simple diagrams, extending Dirac's notation, and connects it to algebraic structures called Strongly Compact Closed Categories, providing a new perspective on quantum theory.

Contribution

It presents a diagrammatic calculus for quantum mechanics and links it to algebraic category theory, offering a novel framework for understanding quantum phenomena.

Findings

Diagrammatic calculus extends Dirac notation

Connection to Strongly Compact Closed Categories

Provides a new algebraic perspective on quantum mechanics

Abstract

These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in quant-ph/0402130 and [4]) which subsumes my Logic of Entanglement quant-ph/0402014. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes quant-ph/0506132. In a last section we provide some pointers to the body of technical literature on the subject.