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Search results for: QUANTUM STATE AND CORRELATIONS BROADCASTING

  • Analytical studies of spectrum broadcast structures in quantum Brownian motion

    Spectrum broadcast structures are a new and fresh concept in the quantum-to-classical transition, introduced recently in the context of decoherence and the appearance of objective features in quantum mechanics. These are specific quantum state structures, responsible for the objectivization of the decohered state of a system. Recently, they have been demonstrated by means of the well-known quantum Brownian motion model of the recoilless...

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  • Quantum key distribution based on private states: Unconditional security over untrusted channels with zero quantum capacity

    Publication
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • D. Leung
    • J. Oppenheim

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2008

    In this paper, we prove unconditional security for a quantum key distribution (QKD) protocol based on distilling pbits (twisted ebits) from an arbitrary untrusted state that is claimed to contain distillable key. Our main result is that we can verify security using only public communication-via parameter estimation of the given untrusted state. The technique applies even to bound-entangled states, thus extending QKD to the regime...

  • Unconditional privacy over channels which cannot convey quantum information

    Publication
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • D. Leung
    • J. Oppenheim

    - PHYSICAL REVIEW LETTERS - Year 2008

    Quantum cryptography enables one to verify that the state of the quantum system has not been tampered with and thus one can obtain privacy regardless of the power of the eavesdropper. All previous protocols relied on the ability to faithfully send quantum states or equivalently to share pure entanglement. Here we show this need not be the case-one can obtain verifiable privacy even through some channels which cannot be used to...

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  • Experimental certification of an informationally complete quantum measurement in a device-independent protocol

    Publication

    - Optica - Year 2020

    Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their d2-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information.Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first...

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  • Direct detection of quantum entanglement

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2002

    Basing on positive maps separability criterion we propose the experimentally viable, direct detection of quantum entanglement. It is efficient and does not require any a priori knowledge about the state. For two qubits it provides a sharp (i.e., “if and only if”) separability test and estimation of amount of entanglement. We view this method as a new form of quantum computation, namely, as a decision problem with quantum data structure.

  • Long-distance quantum communication over noisy networks without long-time quantum memory

    Publication
    • P. Mazurek
    • A. Grudka
    • M. Horodecki
    • P. Horodecki
    • J. Łodyga
    • Ł. Pankowski
    • A. Przysiężna

    - PHYSICAL REVIEW A - Year 2014

    The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension D and transmission...

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  • Zero-knowledge convincing protocol on quantum bit is impossible

    Publication

    - Quantum Journal - Year 2017

    It is one of fundamental features of quantum formalism that o n one hand it provides a new infor- mation processing resources and on the other hand puts funda mental constraints on the processing of quantum information implying “no-go” theorems for cloni ng [1–3], bit commitment [4, 5] and deleting [6] in quantum theory. Here we ask about possibilit y of “zero knowledge” scenario which, for its simplicity, can be considered as...

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  • Quantum Coherence as a Resource

    Publication
    • A. Streltsov
    • G. Adesso
    • M. B. Plenio

    - REVIEWS OF MODERN PHYSICS - Year 2017

    The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics....

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  • Quantum privacy witness

    Publication

    - PHYSICAL REVIEW A - Year 2012

    While it is usually known that the mean value of a single observable is enough to detect entanglement or its distillability, the counterpart of such an approach in the case of quantum privacy has been missing. Here we develop the concept of a privacy witness, i.e., a single observable that may detect the presence of the secure key even in the case of bound entanglement. Then we develop the notion of secret-key estimation based...

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  • Structure of the Resource Theory of Quantum Coherence

    Publication
    • A. Streltsov
    • S. Rana
    • P. Boes
    • R. Eisert

    - PHYSICAL REVIEW LETTERS - Year 2017

    Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between the classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological applications of quantum coherence, and limitations that arise if one is lacking the ability to establish superpositions. An important open problem in this context is a simple characterization...

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  • Teleportation of geometric structures in 3D

    The simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state vectors) and 4 (for complex state vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: geometric analogs of states...

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  • Reexamination of the decoherence of spin registers

    Publication

    - PHYSICAL REVIEW A - Year 2019

    We revisit the decoherence process of a multiqubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register’s behavior but also a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called spectrum broadcast structures....

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  • Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus

    Publication

    A class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For s → ∞ the formalism reduces to ordinary arithmetic and calculus. Accordingly, the limit “non-Newtonian to Newtonian” becomes analogous to the classical limit of a quantum theory

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  • Quantum metrology: Heisenberg limit with bound entanglement

    Publication

    - PHYSICAL REVIEW A - Year 2015

    Quantum entanglement may provide a huge boost in the precision of parameter estimation. However, quantum metrology seems to be extremely sensitive to noise in the probe state. There is an important still open question: What type of entanglement is useful as a resource in quantum metrology? Here we raise this question in relation to entanglement distillation. We provide a counterintuitive example of a family of bound entangled states...

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  • Rotational state-changing collisions of C2H− and C2N− anions with He under interstellar and cold ion trap conditions: A computational comparison

    Publication
    • J. Franz
    • B. P. Mant
    • L. González-Sánchez
    • R. Wester
    • F. A. Gianturco

    - JOURNAL OF CHEMICAL PHYSICS - Year 2020

    We present an extensive range of quantum calculations for the state-changing rotational dynamics involving two simple molecular anions that are expected to play some role in the evolutionary analysis of chemical networks in the interstellar environments, C2H− (X1Σ+) and C2N− (X3Σ−), but for which inelastic rates are only known for C2H−. The same systems are also of direct interest in modeling selective photo-detachment experiments...

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  • Establishing Relationships between Parameters of the controlled Compaction Soil by Using Various In-Situ Tests

    Publication

    - Year 2017

    The aim of research was evaluating reliable correlations between chosen soil parameters describing state of surface layers of soil. The paper presents site comparative tests based on the light falling weight deflectometer (LFWD), the static plate load tester (VSS), the dynamic probing light tester (DPL) and the bearing ratio tester (CBR in-situ) with relationships between soil state parameters. All featured in-situ...

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  • Refined theoretical study of radiative association: Cross sections and rate constants for the formation of SiN

    Publication
    • M. Gustafsson
    • S. Antipov
    • J. Franz
    • G. Nyman

    - JOURNAL OF CHEMICAL PHYSICS - Year 2012

    Radiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory...

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  • Objectivity in the non-Markovian spin-boson model

    Publication

    - PHYSICAL REVIEW A - Year 2017

    Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system...

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  • Collective Uncertainty Entanglement Test

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2011

    For a given pure state of a composite quantum system we analyze the product of its projections onto aset of locally orthogonal separable pure states. We derive a bound for this product analogous to theentropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled statesand it allows us to construct a family of entanglement measures, we shall call collectibility. As thesequantities are experimentally...

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  • A simple test for quantum channel capacity

    Publication

    Based on state and channel isomorphism we point out that semidefiniteprogramming can be used as a quick test for nonzero one-way quantum channelcapacity. This can be achieved by searching for symmetric extensions of statesisomorphic to a given quantum channel. With this method we provide examplesof quantum channels that can lead to high entanglement transmission but stillhave zero one-way capacity, in particular, regions of symmetric...

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  • Swapping Space for Time: An Alternative to Time-Domain Interferometry

    Publication

    Young's double-slit experiment [1] requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for...

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  • Necessary and Sufficient Condition for State-Independent Contextual Measurement Scenarios

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2014

    The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes...

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  • Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds

    Publication

    Local hidden-variable model of singlet-state correlations discussed in M. Czachor, Acta Phys. Polon. A 139, 70, is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a `confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring...

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  • Multimodal Approach For Polysensory Stimulation And Diagnosis Of Subjects With Severe Communication Disorders

    Publication

    is evaluated on 9 patients, data analysis methods are described, and experiments of correlating Glasgow Coma Scale with extracted features describing subjects performance in therapeutic exercises exploiting EEG and eyetracker are presented. Performance metrics are proposed, and k-means clusters used to define concepts for mental states related to EEG and eyetracking activity. Finally, it is shown that the strongest correlations...

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  • Increased Certification of Semi-device Independent Random Numbers using Many Inputs and More Postprocessing

    Publication
    • P. A. Mironowicz
    • A. Tavakoli
    • A. Hameedi
    • B. Marques
    • M. Pawłowski
    • M. Bourennane

    - NEW JOURNAL OF PHYSICS - Year 2016

    Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements...

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  • Noncentrosymmetric Triangular Magnet CaMnTeO6: Strong Quantum Fluctuations and Role of s0 versus s2 Electronic States in Competing Exchange Interactions

    Publication
    • X. Huai
    • E. Acheampong
    • E. Delles
    • M. J. Winiarski
    • M. Sorolla II
    • L. Nassar
    • M. Liang
    • C. Ramette
    • H. Ji
    • A. Scheie... and 3 others

    - ADVANCED MATERIALS - Year 2024

    Noncentrosymmetric triangular magnets offer a unique platform for realizing strong quantum fluctuations. However, designing these quantum materials remains an open challenge attributable to a knowledge gap in the tunability of competing exchange interactions at the atomic level. Here, a new noncentrosymmetric triangular S = 3/2 magnet CaMnTeO6 is created based on careful chemical and physical considerations. The model material...

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  • Towards Resource Theory of Coherence in Distributed Scenarios

    Publication

    - Physical Review X - Year 2017

    The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication....

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  • Unraveling the role of boron dimers in the electrical anisotropy and superconductivity in boron-doped diamond

    Publication

    - CARBON - Year 2024

    We use quantum mechanics (QM) to determine the states formed by B dopants in diamond. We find that isolated B sites prefer to form BB dimers and that the dimers pair up to form tetramers (BBCBB) that prefer to aggregate parallel to the (111) surface in the <110> direction, one double layer below the H-terminated surface double layer. These tetramers lead to metallic character (Mott metal Insulator Transition) with holes in the...

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  • Sensitivity of entanglement decay of quantum-dot spin qubits to the external magnetic field

    Publication

    - PHYSICAL REVIEW A - Year 2014

    We study the decay of entanglement of quantum-dot electron-spin qubits under hyperfine-interaction-mediated decoherence.We show that two-qubit entanglement of a single entangled initial state may exhibit decay characteristic of two disentanglement regimes in a single sample, when the externalmagnetic field is changed. The transition is manifested by the suppression of time-dependent entanglement oscillations which are superimposed...

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  • Quantum dots in gas sensing a review

    Air pollution becomes an increasing problem in the recent years. There is a need to develop more sensitive gas sensors. Much effort has been performed to develop different types of gas sensors, such as electrochemical sensors or polymer sensors. One of the most promising approaches to improve sensors performance is the application of the nanostructures as sensing materials. State of the art of quantum...

  • Spontaneous electron emission vs dissociation in internally hot silver dimer anions

    Referring to a recent experiment, we theoretically study the process of a two-channel decay of the diatomic silver anion (Ag2-), namely the spontaneous electron ejection giving Ag2 + e- and the dissociation leading to Ag- + Ag. The ground state potential energy curves of the silver molecules of diatomic neutral and negative ion were calculated using proper pseudo-potentials and atomic basis sets. We also estimated the non-adiabatic...

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  • Electronic structure and magnetism of samarium and neodymium adatoms on free-standing graphene

    Publication
    • A. Kozub
    • A. Shick
    • F. Máca
    • J. Kolorenč
    • A. Lichtenstein

    - PHYSICAL REVIEW B - Year 2016

    The electronic structure of selected rare-earth atoms adsorbed on a free-standing graphene was investigated using methods beyond the conventional density functional theory (DFT+U, DFT +HIA, and DFT+ED). The influence of the electron correlations and the spin-orbit coupling on the magnetic properties has been examined. The DFT+U method predicts both atoms to carry local magnetic moments (spin and orbital) contrary to a nonmagnetic...

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  • From unextendible product bases to genuinely entangled subspaces

    Publication

    - PHYSICAL REVIEW A - Year 2018

    Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure...

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  • Structural properties of hypothetical CeBa2Cu3O7 compound from LSDA+DMFT calculations

    Publication

    The hypothetical stoichiometric CeBa2Cu3O7 (Ce123) compound, which has not been synthesized as a single phase yet, was studied by the density functional theory (DFT). We utilized a method which merges the local spin density approximation (LSDA) with the dynamical mean-field theory (DMFT) to account for the electronic correlations. The LSDA+DMFT calculations were performed in the high-temperature range. The particular emphasis was...

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  • Jahn-Teller and related conical intersections in the benzene radical cation and the monofluoro derivate

    Publication

    - JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM - Year 2007

    The multi-state multi-mode vibronic interactions in the benzene radical cation and its monofluoro derivative have been investigated theoretically, based on high-level electronic structure calculations for the system parameters and a quantum treatment of the nuclear motion. The available experimental data are well reproduced. The interplay of different vibronic coupling mechanisms is pointed out leading to multiple nonadiabatic...

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  • Entanglement and Nonlocality are Inequivalent for Any Number of Parties

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2015

    Understanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite...

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  • Dynamics of quantum entanglement

    Publication

    - PHYSICAL REVIEW A - Year 2002

    A model of discrete dynamics of entanglement of a bipartite quantum state is considered. It involves a global unitary dynamics of the system and periodic actions of local bistochastic or decaying channel. For initially pure states the decay of entanglement is accompanied by an increase of von Neumann entropy of the system. We observe and discuss revivals of entanglement due to unitary interaction of subsystems. For some mixed states...

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  • INFLUENCE OF SOLID PARTICLE CONTAMINATION ON THE WEAR PROCESS IN WATER LUBRICATED MARINE STRUT BEARINGS WITH NBR AND PTFE BUSHES

    Publication

    This paper reports on a study of the influence of solid particle contamination on the wear process in water-lubricated slide bearings (steel-acrylonitrile-butadiene rubber (NBR) and steel- polytetrafluoroethylene (PTFE)). To compare the wear of the shaft journal and bushes (NBR and PTFE) when lubricated with fresh water and contaminated water, an experiment was carried out to identify key factors that influence the state of wear...

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  • Can Communication Power of Separable Correlations Exceed That of Entanglement Resource?

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2014

    The scenario of remote state preparation with a shared correlated quantum state and one bit of forward communication [B. Dakić et al., Nat. Phys. 8, 666 (2012)] is considered. Optimization of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of the use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by...

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  • Comparison of simplified sum-over-state expressions to calculate resonance Raman intensities including Franck-Condon and Herzberg-Teller effects

    Publication

    Sum-over-state (SOS) expressions to simulate absorption spectroscopy and resonance Raman (RR) scattering including Franck-Condon (FC) and Herzberg-Teller (HT) effects are described. Starting from the general SOS method, several simplified SOS formulae are derived. In particular, within the so-called independent mode displaced harmonic oscillator model, it is shown that including the vibronic structure in the absorption and RR spectra...

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  • Production of singlet oxygen atoms by photodissociation of oxywater

    Publication

    - JOURNAL OF CHEMICAL PHYSICS - Year 2009

    Quantum chemical calculations are reported for the energies of the few lowest electronic singlet states of oxywater along dissociation of the oxygen-oxygen bond into water and singlet oxygen using multistate multireference second-order Møller–Plesset perturbation theory. We compute an energy of 21 kcal/mol to remove one oxygen atom in the lowest singlet state. The two lowest excited singlet states have vertical excitation energies...

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  • General paradigm for distilling classical key from quantum states

    Publication

    - IEEE TRANSACTIONS ON INFORMATION THEORY - Year 2009

    In this paper, we develop a formalism for distilling aclassical key from a quantum state in a systematic way, expandingon our previous work on a secure key from bound entanglement(Horodecki et al., 2005). More detailed proofs, discussion, andexamples are provided of the main results. Namely, we demonstratethat all quantum cryptographic protocols can be recast in away which looks like entanglement theory, with the only changebeing...

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  • Is Digitalization Improving Governance Quality? Correlating Analog and Digital Benchmarks

    Publication

    The digitalization of public governance and the resulting concept of electronic governance is a characteristic feature of contemporary information society. Both can be defined as the process and outcome of digital transformation: transformation of the “analog” version of governance into “digital” governance. Measuring both versions of governance against typical performance measures of efficiency, effectiveness, equity, openness...

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  • The Ellenbogen’s “Matter as Software” Concept for Quantum Computer Implementation: IV. The X@C60 Molecular Building Blocks (MBBs) and Computing System Lifetime Estimation

    Publication

    - Quantum Matter - Year 2016

    The problem of approximate lifetimes of individual X@C60 MBBs and tip-based nanofabricated quantum computing device systems is discussed under the conservative assumption of single-point failure. A single chemical transformation of the C60 cage into high-energy opened o-C60 isomer which forms the communication canal for the low energy transfer of an X atom from X@C60 MBB to the outside environment was studied. According to the...

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  • Spinon excitations in the quasi-one-dimensional S=12 chain compound Cs4CuSb2Cl12

    Publication

    - PHYSICAL REVIEW B - Year 2020

    The spin−1/2 Heisenberg antiferromagnetic chain is ideal for realizing one of the simplest gapless quantum spin liquids (QSLs), supporting a many-body ground state whose elementary excitations are fractional fermionic excitations called spinons. Here we report the discovery of such a one-dimensional (1D) QSL in Cs4CuSb2Cl12. Compared to previously reported S=1/2 1D chains, this material possesses a wider temperature range over...

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  • Structural, physicochemical and anticancer study of Zn complexes with pyridyl-based thiazolyl-hydrazones

    Publication
    • J. B. Araškov
    • N. Maciejewska
    • M. Olszewski
    • A. Višnjevac
    • V. Blagojević
    • H. S. Fernandes
    • S. F. Sousa
    • A. Puerta
    • J. M. Padrón
    • B. B. Holló... and 7 others

    - JOURNAL OF MOLECULAR STRUCTURE - Year 2023

    Thiazolyl-hydrazones (THs) exhibit a wide spectrum of biological activity that can be enhanced by complexation with various metal ions. Zn(II) complexes with α-pyridine-1,3-TH ligands may represent an alternative to the standard platinum-based chemotherapeutics. In addition, they show photoluminescence properties and thus can be regarded as multifunctional materials. In this study, we synthesized and characterized three neutral...

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  • Studies on the solid-liquid equilibria and intermolecular interactions Urea binary mixtures with Sulfanilamide and Sulfacetamide

    Publication

    - JOURNAL OF CHEMICAL THERMODYNAMICS - Year 2021

    The binary phase diagrams of Sulfanilamide-Urea (SN-U) and Sulfacetamide-Urea (SC-U) were measured using differential scanning calorimetry technique (DSC). Both examined mixtures were found to form simple binary eutectics. The limited miscibility in the solid state observed by DSC, proving inability of co-crystallization in new multi-molecular form, was also confirmed using PXRD and FTIR-ATR measurements of solid dispersions...

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  • Low-Cost Behavioral Modeling of Antennas by Dimensionality Reduction and Domain Confinement

    Publication

    - Year 2023

    Behavioral modeling has been rising in importance in modern antenna design. It is primarily employed to diminish the computational cost of procedures involving massive full-wave electromagnetic (EM) simulations. Cheaper alternative offer surrogate models, yet, setting up data-driven surrogates is impeded by, among others, the curse of dimensionality. This article introduces a novel approach to reduced-cost surrogate modeling of...

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  • System information propagation for composite structures

    We study in details decoherence process of a spin register, coupled to a spin environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available...

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  • Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

    Publication

    A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are...

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