Qubits are unit vectors in the Euclidean plane

A 2×2 real matrix representation of complex numbers predicts a Bell-type three-party correlation Τ ≤ 7.66. On the other hand, a 2×2 real matrix representation of unit vectors in the Euclidean plane predicts Τ = 3β_CHSH = 6√2 ≈ 8.49. Experimental results convincingly preclude the use of a real representation of complex numbers in quantum mechanics. Indeed, since the real representation of complex numbers is mathematically equivalent to complex numbers, these experimental results also preclude the use of complex numbers in quantum mechanics. The problem with complex numbers is that they commute. Rather, qubits are faithfully represented as unit vectors in the Euclidean plane, whose basis vectors anti-commute. The eigenvalues of qubits are the bits, +1 and −1. The dot product of two qubits gives the Bell correlation between them. Thus, Bell correlation is the result of Euclidean geometry, quantized by the requirement that the only possible measurements of a matrix are its eigenvalues. Einstein was right to argue against “spooky action at a distance”!