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

Consistent quantum mechanics admits no mereotopology

It is standardly assumed in discussions of quantum theory that physical systems can be regarded as having well-defined Hilbert spaces. It is shown here that a Hilbert space can be consistently partitioned only if its components are assumed not to interact. The assumption that physical systems have well-defined Hilbert spaces is, therefore, physically unwarranted.Comment: 10 pages; to appear in Axiomathe

Rank-based model selection for multiple ions quantum tomography

The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the "sparsity" properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods -- the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) -- to models consising of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of 4 ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a 4 ions experiment aimed at creating a Smolin state of rank 4. The two methods indicate that the optimal model for describing the data lies between ranks 6 and 9, and the Pearson $\chi^{2}$ test is applied to validate this conclusion. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements.Comment: 24 pages, 6 figures, 3 table

Beating noise with abstention in state estimation

We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consists of a number N of identically prepared qubits. We show that the average fidelity of the estimates can increase significantly if the estimation protocol allows for inconclusive answers, or abstentions. We present the optimal such protocol and compute its fidelity for a given probability of abstention. The improvement over standard estimation, without abstention, can be viewed as an effective noise reduction. These and other results are exemplified for small values of N. For asymptotically large N, we derive analytical expressions of the fidelity and the probability of abstention, and show that for a fixed fidelity gain the latter decreases with N at an exponential rate given by a Kulback-Leibler (relative) entropy. As a byproduct, we obtain an asymptotic expression in terms of this very entropy of the probability that a system of N qubits, all prepared in the same state, has a given total angular momentum. We also discuss an extreme situation where noise increases with N and where estimation with abstention provides a most significant improvement as compared to the standard approach

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

β-Arrestins Regulate Protease-activated Receptor-1 Desensitization but Not Internalization or Down-regulation

The widely expressed beta-arrestin isoforms 1 and 2 bind phosphorylated G protein-coupled receptors (GPCRs) and mediate desensitization and internalization. Phosphorylation of protease-activated receptor-1 (PAR1), a GPCR for thrombin, is important for desensitization and internalization, however, the role of beta-arrestins in signaling and trafficking of PAR1 remains unknown. To assess beta-arrestin function we examined signaling and trafficking of PAR1 in mouse embryonic fibroblasts (MEFs) derived from beta-arrestin (betaarr) knockouts. Desensitization of PAR1 signaling was markedly impaired in MEFs lacking both betaarr1 and betaarr2 isoforms compared with wild-type cells. Strikingly, in cells lacking only betaarr1 PAR1 desensitization was also significantly impaired compared with betaarr2-lacking or wild-type cells. In wild-type MEFs, activated PAR1 was internalized through a dynamin- and clathrin-dependent pathway and degraded. Surprisingly, in cells lacking both betaarr1 and betaarr2 activated PAR1 was similarly internalized through a dynamin- and clathrin-dependent pathway and degraded, whereas the beta(2)-adrenergic receptor (beta(2)-AR) failed to internalize. A PAR1 cytoplasmic tail mutant defective in agonist-induced phosphorylation failed to internalize in both wild-type and beta-arrestin knockout cells. Thus, PAR1 appears to utilize a distinct phosphorylation-dependent but beta-arrestin-independent pathway for internalization through clathrin-coated pits. Together, these findings strongly suggest that the individual beta-arrestin isoforms can differentially regulate GPCR desensitization and further reveal a novel mechanism by which GPCRs can internalize through a dynamin- and clathrin-dependent pathway that is independent of arrestins

Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. First, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. We give a new theoretical analysis of compressed tomography, based on the restricted isometry property (RIP) for low-rank matrices. Using these tools, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank.Comment: 16 pages, 3 figures. Matlab code included with the source file

Quantum computing with mixed states

We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits.Comment: 2 figures, 52 reference

Single crystals of LnFeAsO1-xFx (Ln=La, Pr, Nd, Sm, Gd) and Ba1-xRbxFe2As2: growth, structure and superconducting properties

A review of our investigations on single crystals of LnFeAsO1-xFx (Ln=La, Pr, Nd, Sm, Gd) and Ba1-xRbxFe2As2 is presented. A high pressure technique has been applied for the growth of LnFeAsO1-xFx crystals, while Ba1-xRbxFe2As2 crystals were grown using quartz ampoule method. Single crystals were used for electrical transport, structure, magnetic torque and spectroscopic studies. Investigations of the crystal structure confirmed high structural perfection and show less than full occupation of the (O, F) position in superconducting LnFeAsO1-xFx crystals. Resistivity measurements on LnFeAsO1-xFx crystals show a significant broadening of the transition in high magnetic fields, whereas the resistive transition in Ba1 xRbxFe2As2 simply shifts to lower temperature. Critical current density for both compounds is relatively high and exceeds 2x109 A/m2 at 15 K in 7 T. The anisotropy of magnetic penetration depth, measured on LnFeAsO1-xFx crystals by torque magnetometry is temperature dependent and apparently larger than the anisotropy of the upper critical field. Ba1-xRbxFe2As2 crystals are electronically significantly less anisotropic. Point-Contact Andreev-Reflection spectroscopy indicates the existence of two energy gaps in LnFeAsO1-xFx. Scanning Tunneling Spectroscopy reveals in addition to a superconducting gap, also some feature at high energy (~20 meV).Comment: 27 pages, 19 figures, 2 tables, accepted to the special issue of the Physica C on superconducting pnictide