20 research outputs found
Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion
We consider 1-qubit mixed quantum state estimation by adaptively updating
measurements according to previously obtained outcomes and measurement
settings. Updates are determined by the average-variance-optimality
(A-optimality) criterion, known in the classical theory of experimental design
and applied here to quantum state estimation. In general, A-optimization is a
nonlinear minimization problem; however, we find an analytic solution for
1-qubit state estimation using projective measurements, reducing computational
effort. We compare numerically two adaptive and two nonadaptive schemes for
finite data sets and show that the A-optimality criterion gives more precise
estimates than standard quantum tomography.Comment: 15 pages, 7 figure
Trinuclear μ<sub>3</sub>‑Silyl Complexes of Ruthenium and Group 9 Metals Having 3c-2e Interactions and Transformation of a μ<sub>3</sub>‑Silyl Complex of Ru<sub>2</sub>Ir into μ‑Silyl and μ<sub>3</sub>‑Silylene Complexes
μ<sub>3</sub>-Silyl complexes (Cp*Ru)<sub>2</sub>(Cp*M)(μ<sub>3</sub>-H<sub>2</sub>SiR)(μ-H)<sub>3</sub> (<b>4</b>, M = Co; <b>5</b>, M = Rh; <b>6</b>, M = Ir) were synthesized by the
reaction of trinuclear heterometallic clusters of Ru and group 9 metals,
(Cp*Ru)<sub>2</sub>(Cp*M)(μ-H)<sub>3</sub>(μ<sub>3</sub>-H) (<b>1</b>, M = Co; <b>2</b>, M = Rh; <b>3</b>, M = Ir), with primary silanes. The unprecedented coordination mode
of primary silanes on a trimetallic plane was unambiguously confirmed
by means of multinuclear NMR spectroscopy, IR spectroscopy, and X-ray
diffraction studies. The μ-silane complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ-H<sub>2</sub>SiH<sup><i>t</i></sup>Bu)(μ-H)<sub>4</sub> (<b>7</b>), which is a plausible intermediate en route
to the μ<sub>3</sub>-silyl complex, was obtained by the reaction
of <b>3</b> with <sup><i>t</i></sup>BuSiH<sub>3</sub>. The μ<sub>3</sub>-silyl complex <b>6a</b> was transformed
into the μ-silyl complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ-H<sub>2</sub>SiPh)(<sup><i>t</i></sup>BuNC)(μ-H)<sub>3</sub> (<b>8</b>) upon treatment with <sup><i>t</i></sup>BuNC. Complex <b>6a</b> also reacted with CO to afford the
μ<sub>3</sub>-silylene complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ<sub>3</sub>-HSiPh)(μ-CO)(μ-H)<sub>2</sub> (<b>10</b>) via the formation of the μ-silyl complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ-H<sub>2</sub>SiPh)(CO)(μ-H)<sub>3</sub> (<b>9</b>)
Trinuclear μ<sub>3</sub>‑Silyl Complexes of Ruthenium and Group 9 Metals Having 3c-2e Interactions and Transformation of a μ<sub>3</sub>‑Silyl Complex of Ru<sub>2</sub>Ir into μ‑Silyl and μ<sub>3</sub>‑Silylene Complexes
μ<sub>3</sub>-Silyl complexes (Cp*Ru)<sub>2</sub>(Cp*M)(μ<sub>3</sub>-H<sub>2</sub>SiR)(μ-H)<sub>3</sub> (<b>4</b>, M = Co; <b>5</b>, M = Rh; <b>6</b>, M = Ir) were synthesized by the
reaction of trinuclear heterometallic clusters of Ru and group 9 metals,
(Cp*Ru)<sub>2</sub>(Cp*M)(μ-H)<sub>3</sub>(μ<sub>3</sub>-H) (<b>1</b>, M = Co; <b>2</b>, M = Rh; <b>3</b>, M = Ir), with primary silanes. The unprecedented coordination mode
of primary silanes on a trimetallic plane was unambiguously confirmed
by means of multinuclear NMR spectroscopy, IR spectroscopy, and X-ray
diffraction studies. The μ-silane complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ-H<sub>2</sub>SiH<sup><i>t</i></sup>Bu)(μ-H)<sub>4</sub> (<b>7</b>), which is a plausible intermediate en route
to the μ<sub>3</sub>-silyl complex, was obtained by the reaction
of <b>3</b> with <sup><i>t</i></sup>BuSiH<sub>3</sub>. The μ<sub>3</sub>-silyl complex <b>6a</b> was transformed
into the μ-silyl complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ-H<sub>2</sub>SiPh)(<sup><i>t</i></sup>BuNC)(μ-H)<sub>3</sub> (<b>8</b>) upon treatment with <sup><i>t</i></sup>BuNC. Complex <b>6a</b> also reacted with CO to afford the
μ<sub>3</sub>-silylene complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ<sub>3</sub>-HSiPh)(μ-CO)(μ-H)<sub>2</sub> (<b>10</b>) via the formation of the μ-silyl complex (Cp*Ru)<sub>2</sub>(Cp*Ir)(μ-H<sub>2</sub>SiPh)(CO)(μ-H)<sub>3</sub> (<b>9</b>)