Why two qubits are special

We analyze some special properties of a system of two qubits, and in partic ular of the so-called Bell basis for this system, and discuss the possibili ty of extending these properties to higher dimensional systems. We give a g eneral construction for orthonormal bases of maximally entangled vectors, w hich works in any dimension, and is based on Latin squares and complex Hada mard matrices. However, for none of these bases the special properties of t he operation of complex conjugation in Bell basis hold, namely that maximal ly entangled vectors have up-to-a-phase real coefficients and that factoriz able unitaries have real matrix elements. (C) 2000 American Institute of Ph ysics. [S0022- 2488(00)03707-5].