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

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

Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure

The Groverian entanglement measure, G(psi), is applied to characterize a variety of pure quantum states |psi> of multiple qubits. The Groverian measure is calculated analytically for certain states of high symmetry, while for arbitrary states it is evaluated using a numerical procedure. In particular, it is calculated for the class of Greenberger-Horne-Zeilinger states, the W states as well as for random pure states of n qubits. The entanglement generated by Grover's algorithm is evaluated by calculating G(psi) for the intermediate states that are obtained after t Grover iterations, for various initial states and for different sets of the marked states.Comment: 28 pages, 5 figure

Formation of Multipartite Entanglement Using Random Quantum Gates

The formation of multipartite quantum entanglement by repeated operation of one and two qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a non-local geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the non-local geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and non-local interactions between the qubits.Comment: 7 pages, 5 figure

Necessity of Superposition of Macroscopically Distinct States for Quantum Computational Speedup

For quantum computation, we investigate the conjecture that the superposition of macroscopically distinct states is necessary for a large quantum speedup. Although this conjecture was supported for a circuit-based quantum computer performing Shor's factoring algorithm [A. Ukena and A. Shimizu, Phys. Rev. A69 (2004) 022301], it needs to be generalized for it to be applicable to a large class of algorithms and/or other models such as measurement-based quantum computers. To treat such general cases, we first generalize the indices for the superposition of macroscopically distinct states. We then generalize the conjecture, using the generalized indices, in such a way that it is unambiguously applicable to general models if a quantum algorithm achieves exponential speedup. On the basis of this generalized conjecture, we further extend the conjecture to Grover's quantum search algorithm, whose speedup is large but quadratic. It is shown that this extended conjecture is also correct. Since Grover's algorithm is a representative algorithm for unstructured problems, the present result further supports the conjecture.Comment: 18 pages, 5 figures. Fixed typos throughout the manuscript. This version has been publishe

Robust, directed assembly of fluorescent nanodiamonds

© 2016 The Royal Society of Chemistry. Arrays of fluorescent nanoparticles are highly sought after for applications in sensing, nanophotonics and quantum communications. Here we present a simple and robust method of assembling fluorescent nanodiamonds into macroscopic arrays. Remarkably, the yield of this directed assembly process is greater than 90% and the assembled patterns withstand ultra-sonication for more than three hours. The assembly process is based on covalent bonding of carboxyl to amine functional carbon seeds and is applicable to any material, and to non-planar surfaces. Our results pave the way to directed assembly of sensors and nanophotonics devices

A graphene field-effect transistor as a molecule-specific probe of DNA nucleobases

© 2015 Macmillan Publishers Limited. All rights reserved. Fast and reliable DNA sequencing is a long-standing target in biomedical research. Recent advances in graphene-based electrical sensors have demonstrated their unprecedented sensitivity to adsorbed molecules, which holds great promise for label-free DNA sequencing technology. To date, the proposed sequencing approaches rely on the ability of graphene electric devices to probe molecular-specific interactions with a graphene surface. Here we experimentally demonstrate the use of graphene field-effect transistors (GFETs) as probes of the presence of a layer of individual DNA nucleobases adsorbed on the graphene surface. We show that GFETs are able to measure distinct coverage-dependent conductance signatures upon adsorption of the four different DNA nucleobases; a result that can be attributed to the formation of an interface dipole field. Comparison between experimental GFET results and synchrotron-based material analysis allowed prediction of the ultimate device sensitivity, and assessment of the feasibility of single nucleobase sensing with graphene