title: Priority Choice Experimental Two-Qubit Tomography: Measuring One by One All Elements of Density Matrices.
abstract: In standard optical tomographic methods, the off-diagonal elements of a density matrix ρ are measured indirectly. Thus, the reconstruction of ρ, even if it is based on linear inversion, typically magnifies small errors in the experimental data. Recently, an optimal tomography solution measuring all the elements of ρ one-by-one without error magnification has been theoretically proposed. We implemented this method for two-qubit polarization states. For comparison, we also experimentally implemented other well-known tomographic protocols, either based solely on local measurements (of, e.g., the Pauli operators and James-Kwiat-Munro-White projectors) or with mutually unbiased bases requiring both local and global measurements. We reconstructed seventeen separable, partially and maximally entangled two-qubit polarization states. Our experiments show that our method has the highest stability against errors in comparison to other quantum tomographies. In particular, we demonstrate that each optimally-reconstructed state is embedded in an uncertainty circle of the smallest radius, both in terms of trace distance and disturbance. We explain how to experimentally estimate uncertainty radii for all the implemented tomographies and show that, for each reconstructed state, the relevant uncertainty circles intersect indicating the approximate location of the corresponding physical density matrix.
authors.affiliation: Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland.|RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 12, 772 07 Olomouc, Czech Republic.
authors.forename: Karol
authors.initials: K
authors.lastname: Bartkiewicz
authors.affiliation: Institute of Physics of Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 50A, 77207 Olomouc, Czech Republic.
authors.forename: Antonín
authors.initials: A
authors.lastname: Černoch
authors.affiliation: RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. listopadu 12, 772 07 Olomouc, Czech Republic.
authors.forename: Karel
authors.initials: K
authors.lastname: Lemr
authors.affiliation: Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland.|CEMS, RIKEN, 351-0198 Wako-shi, Japan.
authors.forename: Adam
authors.initials: A
authors.lastname: Miranowicz