Optimal, reliable estimation of quantum states

Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE), generally reports an estimate with zero eigenvalues. These cannot be justified. Furthermore, the MLE estimate is incompatible with error bars, so conclusions drawn from it are suspect. I propose an alternative procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues, its eigenvalues provide a bound on their own uncertainties, and it is the most accurate procedure possible. I show how to implement BME numerically, and how to obtain natural error bars that are compatible with the estimate. Finally, I briefly discuss the differences between Bayesian and frequentist estimation techniques.Comment: RevTeX; 14 pages, 2 embedded figures. Comments enthusiastically welcomed

Verifying multi-partite mode entanglement of W states

We construct a method for verifying mode entanglement of N-mode W states. The ideal W state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-party entanglement with M<N, including mixtures of the latter. We specialize to the case N=4 for illustrative purposes. In the optical case, where excitations are photons, our method can be implemented using linear optics.Comment: 11 pages, 12 figure

Minimax mean estimator for the trine

We explore the question of state estimation for a qubit restricted to the $x$-$z$ plane of the Bloch sphere, with the trine measurement. In our earlier work [H. K. Ng and B.-G. Englert, eprint arXiv:1202.5136[quant-ph] (2012)], similarities between quantum tomography and the tomography of a classical die motivated us to apply a simple modification of the classical estimator for use in the quantum problem. This worked very well. In this article, we adapt a different aspect of the classical estimator to the quantum problem. In particular, we investigate the mean estimator, where the mean is taken with a weight function identical to that in the classical estimator but now with quantum constraints imposed. Among such mean estimators, we choose an optimal one with the smallest worst-case error-the minimax mean estimator-and compare its performance with that of other estimators. Despite the natural generalization of the classical approach, this minimax mean estimator does not work as well as one might expect from the analogous performance in the classical problem. While it outperforms the often-used maximum-likelihood estimator in having a smaller worst-case error, the advantage is not significant enough to justify the more complicated procedure required to construct it. The much simpler adapted estimator introduced in our earlier work is still more effective. Our previous work emphasized the similarities between classical and quantum state estimation; in contrast, this paper highlights how intuition gained from classical problems can sometimes fail in the quantum arena.Comment: 18 pages, 3 figure

Single crystal of superconducting SmFeAsO1-xFy grown at high pressure

Single crystals of SmFeAsO1-xFy of a size up to 120 micrometers have been grown from NaCl/KCl flux at a pressure of 30 kbar and temperature of 1350-1450 C using the cubic anvil high-pressure technique. The superconducting transition temperature of the obtained single crystals varies between 45 and 53 K.Obtained crystals are characterized by a full diamagnetic response in low magnetic fields and by a high critical current density in high magnetic fields. Structural refinement has been performed on single crystal. Differential thermal analysis investigations at 1 bar Ar pressure show decomposition of SmFeAsO1-xFy at 1302 C.Comment: 12 pages, 3 tables, 6 figure

A new triclinic modification of the pyrochlore-type KOs2O6 superconductor

A new modification of KOs2O6, the representative of a new structural type (Pearson symbol aP18, a=5.5668(1)A, b=6.4519(2)A, c=7.2356(2)A, space group P-1, no.2) was synthesized employing high pressure technique. Its structure was determined by single-crystal X-ray diffraction. The structure can be described as two OsO6 octahedral chains relating to each other through inversion and forming big voids with K atoms inside. Quantum chemical calculations were performed on the novel compound and structurally related cubic compound. High-pressure X-ray study showed that cubic KOs2O6 phase was stable up to 32.5(2) GPa at room temperature.Comment: 23 pages, 9 figures,6 tables. Accepted for J. Solid State Che

Anisotropy of Superconducting Single Crystal SmFeAsO0.8F0.2 Studied by Torque Magnetometry

Single crystals of the oxypnictide superconductor SmFeAsO0.8F0.2 with T c≃45(1) K were investigated by torque magnetometry. The crystals of mass ≤0.1μg were grown by a high-pressure cubic anvil technique. The use of a high-sensitive piezoresistive torque sensor made it possible to study the anisotropic magnetic properties of these tiny crystals. The anisotropy parameter γ was found to be field independent, but varies strongly with temperature ranging from γ≃8 at T≲T c to γ≃23 at T≃0.4T c. This unusual behavior of γ signals unconventional superconductivit

High Power Impulse Magnetron Sputtering of CIGS Thin Films for High Efficiency Thin Film Solar Cells

In this work CuIn1-xGaxSe2 (CIGS) thin films with three different values of x (0; 0.28; 1) were preparedby nonreactive sputtering of Cu, In and Ga in HiPIMS (High Power Impulse Magnetron Sputtering) orDC magnetron and subsequently selenized in an Ar+Se atmosphere. Optical emission spectroscopy(OES) was used to monitor some basic plasma parameters during sputtering of metallic precursors. CIGSthin film characteristics were measured using X-ray diffraction (XRD), scanning electron microscopy(SEM), Raman spectroscopy, energy-dispersive X-ray spectroscopy (EDX) and other techniques

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic

Bjurböle L/LL4 ordinary chondrite properties studied by Raman spectroscopy, X-ray diffraction, magnetization measurements and Mössbauer spectroscopy

Bjurbole L/LL4 ordinary chondrite was studied using scanning electron microscopy with energy dispersive spectroscopy, Raman spectroscopy, X-ray diffraction, magnetization measurements and Mossbauer spectroscopy. The phase composition and the relative iron fractions in the iron-bearing phases were determined. The unit cell parameters for olivine, orthopyroxene and clinopyroxene are similar to those observed in the other ordinary chondrites. The higher contents of forsterite and enstatite were detected by Raman spectroscopy. Magnetization measurements showed that the temperature of the ferrimagnetic-paramagnetic phase transition in chromite is around 57 K and the saturation magnetic moment is similar to 7 emu/g. The values of the Fe-57 hyperfine parameters for all components in the Bjurbole Mossbauer spectrum were determined and related to the corresponding iron-bearing phases. The relative iron fractions in Bjurbole and the Fe-57 hyperfine parameters of olivine, orthopyroxene and troilite were compared with the data obtained for the selected L and LL ordinary chondrites. The Fe2+ occupancies of the M1 and M2 sites in silicate crystals were determined using both X-ray diffraction and Mossbauer spectroscopy. Then, the temperatures of equilibrium cation distribution were determined, using two independent techniques, for olivine as 666 K and 850 K, respectively, and for orthopyroxene as 958 K and 1136 K, respectively. Implications of X-ray diffraction, magnetization measurements and Mossbauer spectroscopy data for the classification of the studied Bjurbole material indicate its composition being close to the LL group of ordinary chondrites. (C) 2020 Elsevier B.V. All rights reserved.Peer reviewe

Angular dependence of resistivity in the superconducting state of NdFeAsO0.82_{0.82}F0.18_{0.18} single crystals

We report the results of angle dependent resistivity of NdFeAsO$_{0.82}$F$_{0.18}$ single crystals in the superconducting state. By doing the scaling of resistivity within the frame of the anisotropic Ginzburg-Landau theory, it is found that the angle dependent resistivity measured under different magnetic fields at a certain temperature can be collapsed onto one curve. As a scaling parameter, the anisotropy $\Gamma$ can be determined for different temperatures. It is found that $\Gamma(T)$ increases slowly with decreasing temperature, varying from $\Gamma \simeq$ 5.48 at T=50 K to $\Gamma \simeq$ 6.24 at T=44 K. This temperature dependence can be understood within the picture of multi-band superconductivity.Comment: 7 pages, 4 figure