Comment on "Groverian Entanglement Measure and Evolution of Entanglement in Search Algorithm for n(= 3, 5)-Qubit Systems with Real Coefficients" (Volume 6, Number 4, August 2007), by Arti Chamoli and C. M. Bhandari

We point out that the main results-the analytic expressions for the Groverian Measure of Entanglement, in the above mentioned paper are erroneous. The technical mistake of the paper is discussed. It is shown by an explicit example that the formula for calculating the Groverian measure yields G(|\psi>) = 0 for some entangled states.Comment: 4 pages, published online in Quantum Info. Process. on 24 July 200

The Groverian Measure of Entanglement for Mixed States

The Groverian entanglement measure introduced earlier for pure quantum states [O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is generalized to the case of mixed states, in a way that maintains its operational interpretation. The Groverian measure of a mixed state of n qubits is obtained by a purification procedure into a pure state of 2n qubits, followed by an optimization process based on Uhlmann's theorem, before the resulting state is fed into Grover's search algorithm. The Groverian measure, expressed in terms of the maximal success probability of the algorithm, provides an operational measure of entanglement of both pure and mixed quantum states of multiple qubits. These results may provide further insight into the role of entanglement in making quantum algorithms powerful.Comment: 6 pages, 2 figure

Entangled Quantum States Generated by Shor's Factoring Algorithm

The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated during the pre-processing stage of the algorithm and remains nearly constant during the quantum Fourier transform stage. The entanglement is found to be correlated with the speedup achieved by the quantum algorithm compared to classical algorithms.Comment: 7 pages, 4 figures submitted to Phys. Rev.

Novel screening test for celiac disease using peptide functionalised gold nanoparticles

© The Author(s) 2018. Published by Baishideng Publishing Group Inc. All rights reserved. AIM To develop a screening test for celiac disease based on the coating of gold nanoparticles with a peptide sequence derived from gliadin, the protein that triggers celiac disease. METHODS 20 nm gold nanoparticles were first coated with NeutrAvidin. A long chain Polyethylene glycol (PEG) linker containing Maleimide at the Ω-end and Biotin group at the α-end was used to ensure peptide coating to the gold nanoparticles. The maleimide group with the thiol (-SH) side chain reacted with the cysteine amino acid in the peptide sequence and the biotinylated and PEGylated peptide was added to the NeutrAvidin coated gold nanoparticles. The peptide coated gold nanoparticles were then converted into a serological assay. We used the peptide functionalised gold nanoparticle-based assay on thirty patient serum samples in a blinded assessment and compared our results with the previously run serological and pathological tests on these patients. RESULTS A stable colloidal suspension of peptide coated gold nanoparticles was obtained without any aggregation. An absorbance peak shift as well as color change was caused by the aggregation of gold nanoparticles following the addition of anti-gliadin antibody to peptide coated nanoparticles at levels associated with celiac disease. The developed assay has been shown to detect anti-gliadin antibody not only in quantitatively spiked samples but also in a small-scale study on real non-hemolytic celiac disease patient’s samples. CONCLUSION The study demonstrates the potential of gold nanoparticle-peptide based approach to be adapted for developing a screening assay for celiac disease diagnosis. The assay could be a part of an exclusion based diagnostic strategy and prove particularly useful for testing high celiac disease risk populations