Why Two Qubits Are Special

We analyze some special properties of a system of two qubits, and in particular of the so-called Bell basis for this system, which have played an important role in recent papers on entanglement of qubits. In particular, we show which of these properties may be generalized to higher dimension. We give a general construction for bases of maximally entangled vectors in any dimension, but show that none of the properties related to complex conjugation in Bell basis can be realized for higher dimensional analogs.