Achieving quantum precision limit in adaptive qubit state tomography

The precision limit in quantum state tomography is of great interest not only to practical applications but also to foundational studies. However, little is known about this subject in the multiparameter setting even theoretically due to the subtle information tradeoff among incompatible observables. In the case of a qubit, the theoretic precision limit was determined by Hayashi as well as Gill and Massar, but attaining the precision limit in experiments has remained a challenging task. Here we report the first experiment which achieves this precision limit in adaptive quantum state tomography on optical polarization qubits. The two-step adaptive strategy employed in our experiment is very easy to implement in practice. Yet it is surprisingly powerful in optimizing most figures of merit of practical interest. Our study may have significant implications for multiparameter quantum estimation problems, such as quantum metrology. Meanwhile, it may promote our understanding about the complementarity principle and uncertainty relations from the information theoretic perspective.Comment: 9 pages, 4 figures; titles changed and structure reorganise

Error-compensation measurements on polarization qubits

Systematic errors are inevitable in most measurements performed in real life because of imperfect measurement devices. Reducing systematic errors is crucial to ensuring the accuracy and reliability of measurement results. To this end, delicate error-compensation design is often necessary in addition to device calibration to reduce the dependence of the systematic error on the imperfection of the devices. The art of error-compensation design is well appreciated in nuclear magnetic resonance system by using composite pulses. In contrast, there are few works on reducing systematic errors in quantum optical systems. Here we propose an error-compensation design to reduce the systematic error in projective measurements on a polarization qubit. It can reduce the systematic error to the second order of the phase errors of both the half-wave plate (HWP) and the quarter-wave plate (QWP) as well as the angle error of the HWP. This technique is then applied to experiments on quantum state tomography on polarization qubits, leading to a 20-fold reduction in the systematic error. Our study may find applications in high-precision tasks in polarization optics and quantum optics.Comment: 8 pages, 3 figure

2-(2-Hy­droxy-3-meth­oxy­phen­yl)-1H-benzimidazol-3-ium perchlorate

In the title mol­ecular salt, C14H13N2O2 +·ClO4 −, the ring systems in the cation are almost coplanar [dihedral angle = 5.53 (13)°]. Intra­molecular N—H⋯O and O—H⋯O hydrogen bonds generate S(6) and S(5) rings, respectively. In the crystal, the two H atoms involved in the intra­molecular hydrogen bonds also participate in inter­molecular links to acceptor O atoms of the perchlorate anions. A simple inter­molecular N—H⋯O bond also occurs. Together, these form a double-chain structure along [101]

Aqua­cyanido{6,6′-dimeth­oxy-2,2′-[1,2-phenyl­enebis(nitrilo­methanylyl­idene)]diphenolato}cobalt(III) acetonitrile hemisolvate

In the title complex, [Co(C22H18N2O4)(CN)(H2O)]·0.5CH3CN, the CoIII cation is N,N′,O,O′-chelated by a 6,6′-dimeth­oxy-2,2′-[1,2-phenyl­enebis(nitrilo­methanylyl­idene)]diphenolate dianion, and is further coordinated by a cyanide anion and a water mol­ecule in the axial sites, completing a distorted octa­hedral coordination geometry. In the crystal, pairs of bifurcated O—H⋯(O,O) hydrogen bonds link adjacent mol­ecules, forming centrosymmetric dimers. The acetonitrile solvent mol­ecule shows 0.5 occupancy

Poly[tetra­aquadi-μ4-oxalato-potassium­ytterbium(III)]

In the title compound, [KYb(C2O4)2(H2O)4]n, the YbIII ion lies on a site of symmetry in a dodeca­hedral environment defined by eight O atoms from four oxalate ligands. The K atom lies on a different axis and is coordinated by four O atoms from four oxalate ligands and four water O atoms. The oxalate ligand has an inversion center at the mid-point of the C—C bond. The metal ions are linked by the oxalate ligands into a three-dimensional framework. O—H⋯O hydrogen bonding is present in the crystal structure

Aqua­(cyanido-κC){6,6′-dimeth­oxy-2,2′-[o-phenyl­enebis(nitrilo­methanylyl­idene)]diphenolato-κ4 O 1,N,N′,O 1′}cobalt(III) acetonitrile monosolvate

In the title complex, [Co(C22H18N2O4)(CN)(H2O)]·CH3CN, the CoIII ion is six-coordinated in a distorted octa­hedral environment defined by two N atoms and two O atoms from a salen ligand in the equatorial plane and one O atom from a water mol­ecule and one C atom from a cyanide group at the axial positions. O—H⋯O hydrogen bonds connect adjacent complex mol­ecules into dimers. C—H⋯N hydrogen bonds and π–π inter­actions between the benzene rings [centroid–centroid distances = 3.700 (2) and 3.845 (2) Å] are also present

[N,N′-Bis(3-meth­oxy-2-oxidobenzyl­idene)ethyl­enediammonium-κ4 O,O′,O′′,O′′′]tris­(nitrato-κ2 O,O′)dysprosium(III)

In the title mononuclear Schiff base complex, [Dy(NO3)3(C18H20N2O4)], the DyIII ion is ten-coordinated in a distorted hexa­deca­hedral geometry by six O atoms of three nitrate anions and four O atoms of the Schiff base ligand. An intra­molecular N—H⋯O hydrogen bond occurs. The crystal structure is stabilized by inter­molecular C—H⋯O hydrogen bonds

{μ-6,6′-Dimeth­oxy-2,2′-[propane-1,3-diylbis(nitrilo­methyl­idyne)]diphenolato}trinitratocopper(II)europium(III)

In the title complex, [CuEu(C19H20N2O4)(NO3)3], the CuII ion is four-coordinated in a square-planar geometry by two O atoms and two N atoms of the deprotonated Schiff base. The EuIII atom is ten-coordinate, chelated by three nitrate groups and linked to the four O atoms of the deprotonated Schiff base