Qubits and oriented matroids in four time and four space dimensions

TL;DR

This paper explores the relationship between 4-rebits, oriented matroids, and the Nambu-Goto action in a (4+4)-dimensional spacetime, revealing connections between quantum information, geometry, and theoretical physics.

Contribution

It establishes a novel link between 4-rebits, oriented matroids, and high-dimensional spacetime physics, highlighting their geometric and algebraic interrelations.

Findings

4-rebits have the same degrees of freedom as 3-qubits

(4+4)-dimensional spacetime can be split into (3+1) and (1+3) signatures

Geometric aspects of 4-rebits relate to oriented matroid theory

Abstract

We establish a connection between 4-rebits (real qubits) and the Nambu-Goto action with target `spacetime' of four time and four space dimensions ((4+4)-dimensions)). We motivate the subject with three observations. The first one is that a 4-rebit contains exactly the same number of degree of freedom as a complex 3-qubit and therefore 4-rebits are special in the sense of division algebras. Secondly, the (4+4)-dimensions can be splitted as (4+4)=(3+1)+(1+3) and therefore they are connected with an ordinary (1+3)-spacetime and with changed signature (3+1)-spacetime. Finally, we show how geometric aspects of 4-rebits can be related to the chirotope concept of oriented matroid theory.