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We present an error analysis of various tomographic protocols based on thelinear inversion for the reconstruction of an unknown two-qubit state. We solvethe problem of finding a tomographic protocol which is the most robust againsterrors 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 tomographicprotocols, including those based on mutually unbiased bases, are nonoptimal fordetermining all 16 elements of an unknown two-qubit density matrix. Our methodis based on the measurements of the 16 generalized Pauli operators, wheretwelve of them can be locally measured, and the other four require nonlocalBell 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 optimalreconstruction of two photons in an unknown polarization state usingconventional detectors and linear-optical elements. Moreover, we define theoperators for the optimal reconstruction of the states of multiqubit ormultilevel (qudit) systems.

Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers