Qubits and oriented matroids in four time and four space dimensions

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.