The role of preparation in quantum process tomography

In a recent letter one of us pointed out how differences in preparation procedures for quantum experiments can lead to non-trivial differences in the results of the experiment. The difference arise from the initial correlations between the system and environment. Therefore, any quantum experiment that is prone to the influences from the environment must be prepared carefully. In this paper, we study quantum process tomography in light of this. We suggest several experimental setups, where preparation of initial state plays a role on the final outcome of the experiment. We show that by studying the linearity and the positivity of the resulting maps the experimenter can determine the nature of the initial correlations between the system and the environment.Comment: 11 pages, 4 fig

Topological Signal Processing on Quantum Computers for Higher-Order Network Analysis

Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions among nodes, known as higher-order networks. In this context, simplicial complexes are a class of higher-order networks that have received significant attention due to their topological structure and connections to Hodge theory. Topological signal processing utilizes these connections to analyze and manipulate signals defined on non-Euclidean domains such as simplicial complexes. In this work, we present a general quantum algorithm for implementing filtering processes in TSP and describe its application to extracting network data based on the Hodge decomposition. We leverage pre-existing tools introduced in recent quantum algorithms for topological data analysis and combine them with spectral filtering techniques using the quantum singular value transformation framework. While this paper serves as a proof-of-concept, we obtain a super-polynomial improvement over the best known classical algorithms for TSP filtering processes, modulo some important caveats about encoding and retrieving the data from a quantum state. The proposed algorithm generalizes the applicability of tools from quantum topological data analysis to novel applications in analyzing high-dimensional complex systems

Probing high pressure properties of single wall carbon nanotubes through fullerene encapsulation

The high pressure behavior of bundled 1.35±0.1nm diameter single wall carbon nanotubes (SWNT) filled with C70 fullerenes (usually called peapods) has been investigated by Raman spectroscopy and compared with the corresponding behavior of the nonfilled SWNT. We show experimentally that two reversible pressure-induced transitions take place in the compressed bundle SWNT. The first transition, in the 2–2.5GPa range, is in good correspondence with predictions of the thermodynamic instability of the nanotube circular cross section for the studied tube diameter. An interaction between the fullerenes and the tube walls is then observed at about 3.5GPa, which evidences a progressive deformation of the tube cross section. The second transition takes place at pressures between 10 and 30GPa, and is evidenced by two effects by a strong frequency downshift of the Raman transverse modes and the concomitant disappearance of the fullerenes Raman modes in peapods. The pressure at which the second transition takes place is strongly dependent on the nature of the pressure transmitting medium. We also report irreversible effects at high pressure as the shortening of the tubes, the formation of nanostructures and the disappearance of the C70 Raman signal in some cases. Transmission electron microscopy studies are also reported supporting these transformations

Compact Nuclei in Galaxies at Moderate Redshift:II. Their Nature and Implications for the AGN Luminosity Function

This study explores the space density and properties of active galaxies to z=0.8. We have investigated the frequency and nature of unresolved nuclei in galaxies at moderate redshift as indicators of nuclear activity such as Active Galactic Nuclei (AGN) or starbursts. Candidates are selected by fitting imaged galaxies with multi-component models using maximum likelihood estimate techniques to determine the best model fit. We select those galaxies requiring an unresolved point-source component in the galaxy nucleus, in addition to a disk and/or bulge component, to adequately model the galaxy light. We have searched 70 WFPC2 images primarily from the Medium Deep Survey for galaxies containing compact nuclei. In our survey of 1033 galaxies, the fraction containing an unresolved nuclear component greater than 5% of the total galaxy light is 9+/-1% corrected for incompleteness. In this second of two papers in this series, we discuss the nature of the compact nuclei and their hosts. We present the upper limit luminosity function (LF) for low-luminosity AGN (LLAGN) in two redshift bins to z=0.8. Mild number density evolution is detected for nuclei at -18 -16 and this flatness, combined with the increase in number density, is inconsistent with pure luminosity evolution. Based on the amount of density evolution observed for these objects, we find that almost all present-day spiral galaxies could have hosted a LLAGN at some point in their lives. We also comment on the likely contribution of these compact nuclei to the soft X-ray background.Comment: 50 pages, 14 figures, to appear in ApJ, April 199

Completely Positive Maps and Classical Correlations

We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord [H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)]. We prove that initial states that have only classical correlations lead to completely positive reduced dynamics. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present. We outline the implications of our results to quantum process tomography experiments.Comment: 4 pages, 1 figur

Orthorhombic distortion on Li intercalation in anatase

Published versio

Characterization of TiO2 nanoparticles in langmuir-blodgett films

In this work we have synthesized TiO2 nanoparticles, using either a sol–gel base catalysed process in the interior of CTAB reversed micelles (TiO2 CTAB sol), or the neutralization of a TiO2/H2SO4 solution in the interior of AOT reversed micelles. From the absorption and emission data of the TiO2 nanoparticles it is possible to conclude that in the sol–gel route there remains alkoxide groups in the structure, originating transitions lower than the energy gap of TiO2 semiconductor. These transitions disappear in the neutralization procedure, where the alkoxide groups are absent in the structure. We have assigned the observed indirect and direct optical transitions according to the anatase band structure. TiO2 Langmuir-Blodgett (LB) films were prepared either by direct deposition of titanium isopropoxide or by deposition of the TiO2 CTAB sol. These films showed photoluminescence, which was attributed to band-gap emission and to surface recombination of defect states

Operational Significance of Discord Consumption: Theory and Experiment

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this `quantum advantage'. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. No entanglement exists at any point of this experiment. Thus we introduce and demonstrate an operational method to use discord as a physical resource.Comment: 10 pages, 3 figures, updated with Nature Physics Reference, simplified proof in Appendi