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Projected least squares is an intuitive and numerically cheap technique for quantum state tomography: compute the least-squares estimator and project it onto the space of states. The main result of this paper equips this point estimator with rigorous, non-asymptotic convergence guarantees expressed in terms of the trace distance. The estimator’ssample complexityis comparable to the strongest convergence guarantees available in the literature and—in the case of the uniform POVM—saturates fundamental lower bounds. Numerical simulations support these competitive features.

 

A bstract We present a search for the charged lepton-flavor-violating decays ϒ(1 S ) → ℓ ± ℓ ′ ∓ and radiative charged lepton-flavour-violating decays ϒ(1 S ) → γ ℓ ± ℓ ′ ∓ [ ℓ , ℓ ′ = e, μ, τ ] using the 158 million ϒ(2 S ) sample collected by the Belle detector at the KEKB collider. This search uses ϒ(1 S ) mesons produced in ϒ(2 S ) → π + π − ϒ(1 S ) transitions. We do not find any significant signal, so we provide upper limits on the branching fractions at the 90% confidence level. 

A bstract We present the first measurement of the branching fraction of the singly Cabibbo-suppressed (SCS) decay $$ {\Lambda}_c^{+} $$ Λ c + → pη ′ with η ′ → ηπ + π − , using a data sample corresponding to an integrated luminosity of 981 fb − 1 , collected by the Belle detector at the KEKB e + e − asymmetric-energy collider. A significant $$ {\Lambda}_c^{+} $$ Λ c + → pη ′ signal is observed for the first time with a signal significance of 5.4 σ . The relative branching fraction with respect to the normalization mode $$ {\Lambda}_c^{+} $$ Λ c + → pK − π + is measured to be $$ \frac{\mathcal{B}\left({\Lambda}_c^{+}\to p\eta^{\prime}\right)}{\mathcal{B}\left({\Lambda}_c^{+}\to {pK}^{-}{\pi}^{+}\right)}=\left(7.54\pm 1.32\pm 0.73\right)\times {10}^{-3}, $$ B Λ c + → pη ′ B Λ c + → pK − π + = 7.54 ± 1.32 ± 0.73 × 10 − 3 , where the uncertainties are statistical and systematic, respectively. Using the world-average value of $$ \mathcal{B}\left({\Lambda}_c^{+}\to {pK}^{-}{\pi}^{+}\right) $$ B Λ c + → pK − π + = (6 . 28 ± 0 . 32) × 10 − 2 , we obtain $$ \mathcal{B}\left({\Lambda}_c^{+}\to p\eta^{\prime}\right)=\left(4.73\pm 0.82\pm 0.46\pm 0.24\right)\times {10}^{-4}, $$ B Λ c + → pη ′ = 4.73 ± 0.82 ± 0.46 ± 0.24 × 10 − 4 , where the uncertainties are statistical, systematic, and from $$ \mathcal{B}\left({\Lambda}_c^{+}\to {pK}^{-}{\pi}^{+}\right) $$ B Λ c + → pK − π + , respectively.