  We present an error analysis of various tomographic protocols based on the
linear inversion for the reconstruction of an unknown two-qubit state. We solve
the problem of finding a tomographic protocol which is the most robust against
errors in terms of the lowest value (i.e., equal to 1) of a condition number,
as required by the Gastinel-Kahan theorem. In contrast, standard tomographic
protocols, including those based on mutually unbiased bases, are nonoptimal for
determining all 16 elements of an unknown two-qubit density matrix. Our method
is based on the measurements of the 16 generalized Pauli operators, where
twelve of them can be locally measured, and the other four require nonlocal
Bell measurements. Our method corresponds to selectively measuring, one by one,
all of the real and imaginary elements of an unknown two-qubit density matrix.
We describe two experimentally feasible setups of this protocol for the optimal
reconstruction of two photons in an unknown polarization state using
conventional detectors and linear-optical elements. Moreover, we define the
operators for the optimal reconstruction of the states of multiqubit or
multilevel (qudit) systems.

Quantum Physics