Quantum mechanics is *-algebras and tensor networks

TL;DR

This paper introduces a simplified, self-contained tensor network framework for quantum mechanics based on positive *-tensors, enabling intuitive modeling of physical systems and measurement outcomes from an information-theoretic perspective.

Contribution

It presents a novel, mathematically accessible tensor network formalism for quantum mechanics using positive *-tensors, unifying various models within a minimalistic approach.

Findings

Framework effectively models measurement outcomes as network evaluations.

Can represent real-time evolutions and thermal systems within the *-tensor network formalism.

Simplifies categorical quantum mechanics approaches for broader accessibility.

Abstract

We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models translate experimental setups into networks of these *-tensors, and the evaluation of the resulting networks yields the probability distributions describing measurement outcomes. The idea behind our approach is similar to categorical formulations of quantum mechanics. However, our formulation is mathematically simpler and less abstract. Our presentation of the core formalism is completely self-contained and relies on minimal mathematical prerequesites. Therefore, we hope it is in principle also understandable to people without an extensive mathematical background. Additionally, we show how various types of models, like real-time evolutions or thermal systems can be translated into *-tensor networks.